1. A researcher is investigating the effectiveness of a new study-skills training program for elementary school children. A sample of n =25 third-grade children is selected to participate in the program and each child si given a standardized achievement test at the end of the year. For the regular population of third-grade children, scores on the test form a normal distribution with a mean of 150 and a standard deviation of 25. The mean for the sample is M = 158.
a. Identify the independent and the dependent variables for this study.
b. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.
c. Using symbols, state the hypotheses H0 and H1) for the two-tailed test.
d. Sketch the appropriate distribution, and locate the critical region for alpha = .05.
e. Calculate the test statistic (z-score) for the sample.
f. What decision should be made about the null hypothesis, and what decision should be made about the effect of the program?
2. If the alpha level is changed from alpha = .05 to alpha = .01
a. What happens to the boundaries for the critical region?
b. What happens to the probability of a Type 1 error?
3. State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen is obtained and the students are placed in the course during their first semester. One year later, a writing sample is obtained for each student and the writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean = 70.
a. If the writing scores for the population have a standard deviation of 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with alpha = .05.
b. If the population standard deviation is 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with alpha = .05.
c. Briefly explain why you reached different conclusions for part (a) and part (b).
1. What characterizes a regular definition (dictionary) and an operational definition?
2. What is the purpose of sampling?
3. In distributions of populations, please consider Chebyshev’s rule and the Empirical Rule. This takes some thinking.
a) When (what kind of a situation) would you use each in business? Why are they important? How are they calculated?
4. However we need to look closer at “causal research”. Now concerning causal research let us look deeper: What must we actually show (necessary and sufficient conditions) if we are to prove cause and effect?
5. An important practical consideration when sampling is the sample size. So, what determines sample size? What influences our decisions?
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 16 people reveals the mean yearly consumption to be 60 gallons with a standard deviation of 20 gallons.
a.) What is the value of the population mean? What is the best estimate of this value?
b.) Explain why we need to use the t distribution. What assumption do you need to make?
c.) For a 90 percent confidence interval, what is the value of t?
d.) Develop the 90 percent confidence interval for the population mean.
e.) Would it be reasonable to conclude that the population mean is 63 gallons?
I am trying to understand the meaning of data mining? What is data mining? I’m thinking it’s like a huge warehouse that stores data. Is it possible to provide an example? Can you also recommend any literature about data mining?
I would also like to know what type of research situation would use only descriptive statistics? In quantitative only? Is there any published literature I may review from?
What exactly is a regression line and a regression analysis? How can I effectively understand and utilize regression analysis in a research study? Are there any journals or websites I may look at for clarity purposes?
I’m just looking for a better understand of these topics, because the readings seem to technical.
Scatterplots show ________linear relationship.
1. Now is there any way you personally use statistics not related to business. For example when driving somewhere do you ever estimate the time it will take (and possibly include a plus or minus value)?
2. What is the definition of the statistical term variance?
3. “Descriptive statistics is concerned with summarizing data collected from past events.”
Inferential statistics is computing the chance that something will occur in the future. Statistical inference deals with conclusions about a population based on a sample taken from that population. Can you give us an example from your business or work area?
4. In your own words what is the importance of Bayes Theorem to business, science, and us? In other words why should we care?
5. What are the most important concepts of descriptive statistics and probability distributions?
What would you recommend to your management/leadership based on descriptive statistics and probability distributions?
How will descriptive statistics and probability distributions impact you personally and professionally?
What is the value-added from descriptive statistics and probability distributions or what difference can these concepts make to your organization? (e.g., financial savings, productivity improvements, expanded marketing activities).
Of the exploratory, formalized, and casual research designs types, which would you use to assess the effectiveness of an aspect of a computer technician , explain.
1. The maximum number of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data
8 10 11 11 8 9 7 7 7 7 7 7 8
Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The mode is _______
(Type an integer or decimal rounded to the nearest tenth as Needed.)
B. The data does not have a mode.
2. Decide which method of data collection you would use to collect data for study.
A. Experiment
B. Observational study
C. Survey
D. Simulation
3. The number of wins for each team in a league last year are listed. Make a frequency distribution for the data set (Use your classes of width 2 starting at 3). Then approximate the population mean and the population standard deviation of the data set.
4 6 10 4 8 3 3 4 3 4
9 5 4 5 5 6 7 3 4 3
Class f
3-4 _____
5-6 _____
7-8 ______
9-10 ______
The population Mean is approximately u=_______ (_Simplify your answer.)
The population standard deviation is approximately o= _______.
(Round to the nearest hundredth as needed).
4. A Magazine asks its readers to call in their opinion regarding the amount of advertising in the present issue. What type of sampling is used?
A. Systematic
B. Stratified
C. Simple Random
D. Convenience
5. Determine whether the variable is a Qualitative or Quantitative.
Gallons of water in a swimming pool.
Is the variable Qualitative or Quantitative?
A. Qualitative
B. Quantitative
6. Determine whether the approximate shape of the distribution in a histogram is Symmetric, uniform, Skewed left, Skewed right, or none of these.
Choose the best answer below.
A. Skewed left
B. Symmetric
C. Skewed right
D. Uniform
7. The following appear on a physician’s intake form. Identify the level of measurement of the data.
a. temperature b. marital status c. change in health (scale of -5 to 5).
a. What is the level of measurement for temperature?
A. Interval
B. Ratio
C. Ordinal
D. Normal
8. The data show the number of hours of televisions watched per day by a sample of 11 people.
a. Find the data set’s first, second, and the quartiles.
b. Draw a box-and whisker plot that represents the data set.
Find the three quartiles.
Q1 = _________
Q2 = _________
Q3 = ______
9. The Gallup organization contracts 2871 male university graduates who have a white collar job and asks whether or not they had received a raise at work during the past 4 months.
What is the population of the study?
A. Male university graduates who have received a raise at work.
B. Male university graduates who have a white collar job.
C. Male university graduates.
D. Male university graduates who have a white collar job and have received a raise at work.
Statistics
1. The general form of the multiple regression equation is the following:
y = a + b1x1 + b2x2 + b3x3 + ….. + bnxn
“a” is the intercept value defined as the value of y (dependent variable) if all independent variables are equal to zero
“b1” is the sensitivity of y to variable x1. If x1 is varied by 1 unit, y will vary by b1 units
“b2” is the sensitivity of y to variable x2. If x2 is varied by 1 unit, y will vary by b2 units
“b3” is the sensitivity of y to variable x3. If x3 is varied by 1 unit, y will vary by b2 units
Why the coefficients of the independent variable b1, b2 are called sensitivity coefficients?
International Finance
2. What is your opinion of the alternative goal of the firm, to balance the interests of the shareholders and the stakeholders? Do you agree with this view? Why or Why not?
3. A fancy way of saying the difference in yield or interest rates for a bond that will mature in perhaps 30 years versus a bond that will mature in 10 years or 1 year. You can create a graph to show this difference.
With this in mind, please do research on the internet and post the yield to maturity for a 1 year US Treasury Bond, a 10 year US Treasury Bond. Then find the yield to maturity for comparable Gilt. Gilts are the name for UK Government bonds. So you would locate the yield for a 1 year Gilt and a 10 year Gilt.
4. It is hard to believe a competitor is a stakeholder. Isn’t the goal of competition to win and perhaps even dominate the market? If so, how can a company have an interest in the ongoing health of their competitors (except to beat them?) How is a competitor a stakeholder?
1. How would you apply probability concepts, such as confidence intervals and point estimation principles, to make sound business decisions where there are conditions of uncertainty (risk). Pick a specific example from your own area of business experience.
2. Does good research always result in decisions that ..Mobilize the organization to take appropriate actions that, in turn, maximize business performance”? Why?
3. Now to good business research characteristics. Consider: “good business research would be research that seeks out the problems underneath the problems, one that seeks out a true solution to help the company. We would expect this to require precise planning and data acquisition. “. From this we have:
â?¢ addresses the real problem not symptoms
â?¢ provides a solution
â?¢ precise planning
â?¢ data acquisition
These are some but are they sufficient to give us good business research? what else is needed
4. Consider, “Inductive reasoning does not have the strength of relationship between reasoning and conclusion that deductive reasoning does. â??Why is this? Surely there must be a relationship between reason and conclusion in inductive logic.
5. Consider, can we always create an inductive logic example if we have a deductive logic example ? explain.
6. Consider “600 sounds like a feasible sample size, but it is all relative to the size of the customer base. “
Why care?
78. Consider the system of components connected as in the accompanying picture…
Please see attached.
7. The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P) indexes are both used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. The closing prices for the DJIA and the S&P 500 for 10 weeks, beginning Feb 11/2000, follow(Barron’s, April 17, 2000).
Date-DJIA-S&P
Feb 11-10452-1387
Feb 18-10220-1346
Feb 25-9862-1333
Mar 3-10367-1409
Mar 19-9929-1395
Mar 17-10595-1464
Mar 24-11113-1527
Mar 31-10922-1499
Apr 7-11111-1516
Apr 14-10306-1357
a. Develop a scatter diagram for these data with DJIA as the independent variable.
b. Develop the least squares estimated regression equation.
c. Suppose the closing price for the DJIA is 11000. Estimate the closing price for the S&P 500.
1. (10 points) The Pizza Company claims they will deliver your in less than 30 minutes. An undercover consumer reporter monitored a random sample of 30 pizza deliveries at a National outlet. The number of minutes to perform the delivery is reported below.
44, 12, 22, 31, 26, 22, 30, 26, 18, 28, 12, 40, 17, 13, 14, 17, 25, 29, 15, 30, 10, 28, 16, 33, 24, 20, 29, 34, 23, 13.
a. Construct a stem-and-leaf display for the data set.
b. Construct a box plot for the data set.
c. Draw conclusions about the data (e.g. are there any outliers, etc., etc.).
2. (10 points) A manufacturer of PC’s purchases a particular microchip, called the LS-24, from three suppliers: Ball Electronics, Zuller Sales, and Crawford Components. 30 percent of the LS-24 chips are purchased from Ball Electronics, 25 percent from Zuller Sales, and the remaining 45 percent from Crawford Components. The manufacturer has extensive histories on the three suppliers and knows that 4 percent of the LS-24 chips from Ball Electronics are defective, 5 percent of chips from Zuller Sales are defective, and 3 percent of the chips purchased from Crawford Components are defective. When the LS-24 chips arrive at the manufacturer, they are placed directly in a bin and not inspected or otherwise identified by supplier. A worker selects a chip for installation in a PC and finds it defective. What is the probability that it was manufactured by Crawford Components?
3. (10 points) Six percent of the worm gears produced by an automatic, high-speed Barter-Cell milling machine are defective.
a. Among ten randomly selected worm gears, how likely is it that only one is defective?
b. Among ten randomly selected worm gears, what is the probability that at least two are defective?
c. If the worm gears are examined one by one, what is the probability that at most five must be selected to find four that are not defective?
4. (10 points) The article “Reliability of Domestic Waste Biofilm Reactors” (J. of Envir. Engr., 1995: 785-790) suggests that substrate concentration (mg/cm^3) of influent to a reactor is normally distributed with  = 0.30 and  = 0.06.
a. What is the probability that the concentration exceeds 0.355?
b. What is the probability that the concentration is at most 0.273?
c. What is the probability that the concentration is between 0.27 and 0.31?
d. How would you characterize the largest 5% of all concentration levels?
5. (10 points) Let X1, X2, … , X100 denote the actual net weights of 100 randomly selected 50-lb bags of fertilizer.
a. If the expected weight of each bag is 50-lb and the standard deviation is 1.5-lb, calculate P(49.5  X bar  50.25).
b. If the expected weight of each bag is 49.8-lb rather than 50-lb, so that on average bags are under-filled, but the standard deviation is still 1.5-lb, calculate P(49.5  X bar  50.25).
6. (10 points) The Arizona Wildcats baseball team, a minor league team in the Pittburgh Indians organization, plays 75% of their games at night, and 25% during the day. The team wins 55% of their night games, and 85% of their day games. According to today’s newspaper, they won yesterday. What is the probability the game was played at night?
A study was conducted comparing female adolescents who suffer from bulimia (an eating disorder) to healthy females with similar body compositions and levels of physical activity. Listed below are measures of daily caloric intake, recorded in kilocalories per kilogram body weight, for samples of adolescents from each group.
Daily Caloric Intake (kcal/kg)
Bulimic Healthy
15.9 18.9 25.1 20.7 30.6
16.0 19.6 25.2 22.4 33.2
16.5 21.5 25.6 23.1 33.7
17.0 21.6 28.0 23.8 36.6
17.6 22.9 28.7 24.5 37.1
18.1 23.6 29.2 25.3 37.4
18.4 24.1 29.7 25.7
18.9 24.5 30.9 30.6
a) Construct histograms from the values of daily caloric intake for each group (use frequency as the y-axis).
b) Compute mean, median, mode, standard deviation, and range of the daily caloric intake for the bulimic adolescents.
c) Compute mean, median, mode, standard deviation, and range of the daily caloric intake for the healthy adolescents.
d) Is a typical value of daily caloric intake larger for the individuals suffering from bulimia or for the healthy adolescents? Which group has a greater amount of variability in the measurements?
Question 2: Using the normal approximation to the binomial to approximate the probability that X is at least 10, the area under the normal curve should be calculated from?
Question 1: A die was tossed. Given that an even number occurred, the probability that it was a 4 is?
Question 3: A coin is tossed 1,000 times. The probability that at least one head appears is?
See the attached file.
“It is a well-established fact of American political life that young voters are not dependable voters. In a close election, however, the support of even low-turnout groups can be decisive. Thus, Obama’s campaign team apparently decided that his visits to college campuses this week could pay off if he is able to motivate and inspire young voters who already support him to get out and vote in November. Romney’s agreement on the issue of freezing student-loan interest rates was no doubt an attempt to avoid leaving the youth vote totally to Obama. It is clear at this point, however, that Romney has greater potential payoff with more politically active older voters, among whom his support is much stronger.”
a. Present a cross tabulation containing absolute and relative frequencies of the poll – candidate preference by age group.
b. Determine statistical significance and strength of association for the relationship.
Complete problem and chart on MS Word also attached.
A set of final examination grades in an introductory quantitative analysis course is normally distributed, with a mean of 73 and a standard deviation of 8.
a) What is the probability of getting a grade below 91 on this exam?
b) What is the probability that a student scored between 65 and 89?
c) The probability is 5% that a student taking the test scores higher than what grade?
If the professor grades on a curve (that is, gives A’s to the top 10% of the class, regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam, where the mean is 62 and the standard deviation is 3? Please explain your answer statistically only.
1. If 10% of a population of parts is defective, what is the probability of randomly selecting 80 parts and finding that 12 or more parts are defective?
2. A survey was taken of U.S. companies that do business with firms in India.
One of the questions on the survey was: Approximately how many years has your company been trading with firms in India? A random sample of 44 responses to this question yielded a mean of 10.455 years. Suppose the population standard deviation for this question is 7.7 years. Using this information, construct a 90% confidence interval for the mean number of years that a company has been trading in India for the population of U.S. companies trading with firms in India
3. A clothing company produces men jeans. The jeans are made and sold with either a regular cut or a boot cut. In an effort to estimate the proportion of their men jeans market in Oklahoma City that prefers boot-cut jeans, the analyst takes a random sample of 212 jeans sales from the company to Oklahoma City retail outlets. Only 34 of the sales were for boot-cut jeans. Construct a 90% confidence interval to estimate the proportion of the population in Oklahoma City who prefer boot-cut jeans.
4. In an attempt to determine why customer service is important to managers in the United Kingdom, researchers surveyed managing directors of manufacturing plants in Scotland.* One of the reasons proposed was that customer service is a means of retaining customers. On a scale from 1 to 5, with 1 being low and 5 being high, the survey respondents rated this reason more highly than any of the others, with a mean response of 4.30. Suppose U.S.
Researchers believe American manufacturing managers would not rate this reason as highly and conduct a hypothesis test to prove their theory. Alpha is set at .05. Data are gathered and the following results are obtained. Use these data and the eight steps of hypothesis testing to determine whether U.S. managers rate this reason significantly lower than the 4.30 mean ascertained in the United Kingdom. Assume from previous studies that the population standard
deviation is 0.574.
3 4 5 5 4 5 5 4 4 4 4 4 4 4 4 5 4 4 4 3 4 4 4 3 5 4 4 5 4 4 4 5 5
5. A study is conducted using only Boeing 737s traveling 500 miles on comparable routes during the same season of the year. Can the number of passengers predict the cost of flying such routes? It seems logical that more passengers result in more weight and more baggage, which could, in turn, result in increased fuel consumption and other costs. The data are the costs and associated number of passengers for twelve 500-mile commercial airline flights
using Boeing 737s during the same season of the year. Based on the results given below, answer
the following questions.
a) Check the conditions for a hypothesis test and CI of slope.
b) Test to see if there is a significant relationship between the 2 variables.
c) Construct and interpret a 95% CI for the slope.
d) Suppose a flight gets 75 passengers. What would their expected GPA be? Is this a good estimate? Explain in terms of R-sq
I downloaded all of the problems separately and just need a mapping into the instructors grading key,
Can someone please help with this?
I think there is one problem without a solution.
And I really need the formulas spelled out so I can replicate them.
Thanks
1- How do dependent and independent samples differ? Give two examples of dependent samples as they may occur in a business or industry that is familiar to you. Some people use the term paired samples instead of dependent samples.
2 – What is the importance of using STOH in solving problems related to business and operations management? Provide specific examples (preferably from your experience area. Clearly state the null and alternative hypothesis.
3 – Why is the ANOVA (one factor and two factors) important? How can it be used in your profession? Provide examples. Indicate the factors (treatments) and state the hypotheses tested.
4 -What are examples (at least 2) where non-parametric tests are used to analyze business or operations management related problems in general and why use non-parametric tests instead of parametric tests? Provide examples and explain what you are looking for when you conduct these tests. Examples
5. Conduct one- and two-sample tests of hypotheses.
â?¢ What are the most important concepts you have learned from conduct one-and two-sample tests of hypotheses?
â?¢ What would you recommend to your management/leadership based conduct one-and two-sample tests of hypotheses?
â?¢ How will conduct one-and two-sample tests of hypotheses impact you personally and professionally?
â?¢ What are the value-added conduct one- and two-sample tests of hypotheses or what difference can these concepts make to your organization? (e.g., financial savings, productivity improvements, expanded marketing activities).
When pollsters report results of a poll, they often include the margin of error but not much more.
If candidate X has 54% support of the voters with a margin of error of 3%, that means the candidate is predicted to have between 51% and 57% support in the election.
Before jumping to conclusions, what other information would you like the pollster to provide?
I need help understanding how to calculate the problems below. I would like to see the steps taken to find the solution (not just formulas excel provides). Thanks
1. At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden was told, “You can average more than $20 a day in tips.” Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $24,85, with a standard deviation of $3.24. Can Ms. Brigden be 99% confident that she is earning an average of more than $20 per day in tips?
2. The Gibbs Baby Food Company wants to compare the weight gain of infants using their brand versus their competitor’s. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. The standard deviation of the sample was 2.3 pounds. A sample of 55 babies using the competitor’s brand revealed a mean increase in weight of 8.1 pounds in the first three months after birth, with a standard deviation of 2.9 pounds. Can Gibbs be 95% certain that babies using their products gained less weight?
3. Stargell Research Associates conducted a study of the radio listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 35 minutes per day. The standard deviation of the sample of the 10 men studied was 10 minutes per day. The mean listening time for the 12 women studied was also 35 minutes, but the standard deviation of the sample was 12 minutes. Can Stargell be 90% certain that there is a difference in the variability of the listening times for men and women?
4. Shank’s, Inc., a nationwide advertising firm, wants to know whether the size of an advertisement and the color of the advertisement make a difference in the response of magazine readers. A random sample of readers is shown ads of four different colors and three different sizes. Each reader is asked to give the particular combination of size and color a rating between 1 and 10. Assume that the ratings are approximately normally distributed. The rating for each combination is shown in the table following (for example, the rating for a small red ad is 2). Is there a difference in the effectiveness of an advertisement by color and by size? Use the 0.05 level of significance.
Color of Ad
Size of Ad Red Blue Orange Green
Small 2 3 3 6
Medium 3 5 6 7
Large 6 7 8 8
Need help with chapter review questions attached.
I need help understanding how to calculate the problems below. I would like to see the steps taken to find the solution (not just formulas excel provides). Thanks
1. At the time she was hired as a server at the Grumney Family restaurant, Beth Brigden was told, “You can average more than $20 a day in tips.” Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $24,85, with a standard deviation of $3.24. Can Ms. Brigden be 99% confident that she is earning an average of more than $20 per day in tips?
2. The Gibbs Baby Food Company wants to compare the weight gain of infants using their brand versus their competitor’s. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. The standard deviation of the sample was 2.3 pounds. A sample of 55 babies using the competitor’s brand revealed a mean increase in weight of 8.1 pounds in the first three months after birth, with a standard deviation of 2.9 pounds. Can Gibbs be 95% certain that babies using their products gained less weight?
3. Stargell Research Associates conducted a study of the radio listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 35 minutes per day. The standard deviation of the sample of the 10 men studied was 10 minutes per day. The mean listening time for the 12 women studied was also 35 minutes, but the standard deviation of the sample was 12 minutes. Can Stargell be 90% certain that there is a difference in the variability of the listening times for men and women?
4. Shank’s, Inc., a nationwide advertising firm, wants to know whether the size of an advertisement and the color of the advertisement make a difference in the response of magazine readers. A random sample of readers is shown ads of four different colors and three different sizes. Each reader is asked to give the particular combination of size and color a rating between 1 and 10. Assume that the ratings are approximately normally distributed. The rating for each combination is shown in the table following (for example, the rating for a small red ad is 2). Is there a difference in the effectiveness of an advertisement by color and by size? Use the 0.05 level of significance.
Color of Ad
Size of Ad Red Blue Orange Green
Small 2 3 3 6
Medium 3 5 6 7
Large 6 7 8 8
Q1: Using regression techniques, we can plot a scatter diagram and plot a line to the data using the Least Squares method. Generally, the points do not fall directly on the line. Why does this happen? Is it a problem? Explain the parameters in a linear regression line with the aid of co-ordinate axis. How could you say, if the slope is negative, positive, or zero just by looking at the plotted data [Hint: using the independent and dependent relationship]?
Q2: The t statistic and the partial F statistic are, closely related. Explain this relationship. Which would you prefer to use?
1. A study is being undertaken of companies going public. Of particular interest is the relationship between the size of the offering and the price per share. A sample of ten companies that recently went public revealed:
Size Price
(millions) Per Share
Company X Y X2 XY
1 9.0 15.8 81.00 142.20
2 94.4 11.3 8,911.36 1,066.72
3 27.3 13.2 745.29 360.36
4 179.2 10.1 32,112.64 1,809.92
5 71.9 11.1 5,169.61 798.09
6 97.9 11.0 9,584.41 1,076.90
7 93.5 10.9 8,742.25 1,019.15
8 70.0 11.7 4,900.00 819.00
9 160.7 10.3 25,824.49 1,655.21
10 96.5 11.6 9,312.25 1,119.40
Total: 900.4 117.0 105,383.3 9,866.95
a. Determine the regression equation (show your work).
ROW X SQUARED?
b. What does the slope of the regression equation tell us?
10?
c. What would you predict the price per share to be if 95 million shares were offered?
WHAT IS THE FORMULA FOR THIS?
A sample of 65 observations is selected from one population. The sample mean is 2.67 and the
sample standard deviation is 0.75. A sample of 50 observations is selected from a second population.
The sample mean is 2.59 and the sample standard deviation is 0.66. Conduct the following
test of hypothesis using the .08 significance level.
H0: μ1≤ μ2
H1: μ1 > μ2
a. Is this a one-tailed or a two-tailed test?
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding H0?
e. What is the p-value?
Note: Use the five-step hypothesis testing procedure
to solve the following exercises.
See attached file.
A recent national survey reports that the general population gives the president an average rating of µ = 62 on a scale of 1 to 100. A researcher suspects that college students are likely to be more critical of the president than people in the general population. To test these suspicions, a random sample of college students is selected and asked to rate the president. The data for this sample are as follows: 44, 52, 24, 45, 39, 57, 20, 38, 78, 74, 61, 56, 49, 66, 53, 49, 47, 88, 38, 51, 65, 47, 35, 59, 23, 41, 50, 19.
For this problem, you are to calculate standard deviation in written form using the table on page 3. Once you are done with your calculations, enter the data above into the Excel program and cut and paste your output table onto page 4. Your written work for your standard deviation should match or come close to your Microsoft Excel output. Once you are done calculating descriptive statistics, perform a hypothesis test by typing in your responses on page 5 in this document.
a. Using the data listed above in problem 1, calculate by hand the standard deviation.
b. Using Microsoft Excel, type ‘Ratings’ in column A, cell 1. Below cell one, start typing your data in the A column.
c. Hypothesis Testing: Now that you have calculated your descriptive statistics to the data above, you will be able to use your results and perform a hypothesis test. In your results: state an appropriate null hypothesis, indicate the level of significance, identify the critical value, calculate the test statistic, evaluate the test statistic in light of the critical value, and make a decision about the null hypothesis.
A. Problem 1: President Ratings
Written work: Calculate standard deviation
Scores/Values Deviations Mean
(average)Deviation Variance
Squared Deviations Standard Deviation
N =
(X) (X – Mean)
Please see the attached file for the 2 problems. Thank you.
What are the functions of statistics, how do you describe these functions
1. The following list is of measured lifetimes (in thousands of hours) of a sample of a certain machine component.
5.6 4.1 6.0 5.8 5.2 4.3 6.4 5.5 6.0 5.1 4.9 4.2
4.8 6.8 5.6 5.2 7.3 5.4 4.7 5.9 5.0 6.3 4.4 6.0
(i) Group the data into classes, and draw a frequency distribution table. ( ues the classes 4.0-4.4, 4.9 etc.)
(ii) Construct a histogram and frequency polygon of the data.
(iii) Find the median, and upper and lower quartiles and use them to draw a box and whisker plot of the data.
(iv) Find the mean and standard deviation of the data.
(v) Using your frequency distribution table determine what proportion of components you would expect to last at least 5000 hours? do not assume normal distribution.
2. The following table gives the average cost per unit of an item at different levels of production.
Production Level Cost per Unit
800 30
1000 28
1200 27
1400 27
1600 26
(i) Construct a scatter plot of cost as a function of production level.
(ii) Find the equation for the linear regression equation that predicts average cost from production level.
(iii) If a production run of 1500 was planned, what is the expected average cost per unit?
(iv) Calculate the correlation co-efficient for this data and comment on it.
42. During recent seasons, Major League Baseball has been criticized for the length of the
games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample
of 17 games revealed the following times to completion. (Note that the minutes have
been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes
is reported at 2.40 hours.
Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05
significance level.
22. Banner Mattress and Furniture Company wishes to study the number of credit applications
received per day for the last 300 days. The information is reported on the next page.
To interpret, there were 50 days on which no credit applications were received, 77 days
on which only one application was received, and so on. Would it be reasonable to conclude
that the population distribution is Poisson with a mean of 2.0? Use the .05 significance
level. Hint: To find the expected frequencies use the Poisson distribution with a
mean of 2.0. Find the probability of exactly one success given a Poisson distribution with
a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the
number of days in which there was exactly one application. Determine the expected frequency
for the other days in a similar manner.
42. Martin Motors has in stock three cars of the same make and model. The president would
like to compare the gas consumption of the three cars (labeled car A, car B, and car C)
using four different types of gasoline. For each trial, a gallon of gasoline was added to
an empty tank, and the car was driven until it ran out of gas. The following table shows
the number of miles driven in each trial.
Using the .05 level of significance:
a. Is there a difference among types of gasoline?
b. Is there a difference in the cars?
(See the attached file).
Assignment :
Baseball 2005…
Northewest Airlines..
Grocery Stores…
Health Costs …
Major League …
Income Spent on Housing…
I edited the remaining questions
(Please see the attached file)
1 — What are the key points to consider when determining sample size? Why be concerned about determining the size of the sample? Explain.
2 –What is the impact of non-response to research efforts (positive or negative) and what measures can be undertaken to prevent its effects on primary data collection? Explain.
3 –Why is the level of measurement important in research? Explain. Identify and give an example of each.
4 –Discuss and expand upon what is needed for validity and reliability of samples, and then discuss the following type of popular proportion statement: SPAM is favored in the polls by 82% (margin of error +/- 4%) over steaks. How can this be JUNK statistics? (Use technical reasoning; your â??gutâ? does not count) Assume the values used to determine margin of error are done correctly. Explain answer.
5. Construct effective questionnaires and surveys
â?¢ What are the most important concepts you have learned from construct effective questionnaires and surveys?
â?¢ What would you recommend to your management/leadership based construct effective questionnaires and surveys?
â?¢ How will construct effective questionnaires and surveys impact you personally and professionally?
â?¢ What are the value-added construct effective questionnaires and surveys or what difference can these concepts make to your organization? (e.g., financial savings, productivity improvements, expanded marketing activities).
Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86. (a) Construct a 90 percent confidence interval for the proportion of all kernels that would not pop. (b) Check the normality assumption. (c) Try the Very Quick Rule. Does it work well here? Why, or why not? (d) Why might this sample not be typical?
Discusses and identify each data (survey question) as to type (rating, ranking, and category).
1. What characterizes ‘good business research’. Emphasis is on good.
2. What is the relationship between deductive and inductive arguments (reasoning)? Are both types of arguments (reasoning) valuable in research? Explain. Provide examples of each type of argument, illustrating the benefits of their usage.
3. How would you apply probability concepts, such as confidence intervals and point estimation principles, to make sound business decisions where there are conditions of uncertainty (risk). Pick a specific example from your own area of business experience.
4. Apply concepts of probability to business decisions
What are the most important concepts you have learned from apply concepts of probability to business decisions?
What would you recommend to your management/leadership based apply concepts of probability to business decisions?
How will apply concepts of probability to business decision impact you personally and professionally?
What is the value-added apply concepts of probability to business decisions or what difference can these concepts make to your organization? (e.g., financial savings, productivity improvements, expanded marketing activities).
As part of the US Environmental Protection Agency’s (EPA) efforts to “protect human health and safeguard the natural environment,” the EPA conducts the Urban Air Toxics Monitoring Program (UATMP). The program has gathered thousands of air samples and analyzed them for concentrations of more than 50 different organic compounds, such as formaldehyde. Formaldehyde is also found in the smoke from forest fires, automobile exhaust, and tobacco smoke. The results from UATMP are used to gain insight to the effects of air pollution and determine if efforts to clean up the air are working.
For instance, using air samples from a major city, the EPA can analyze the results and estimate the mean concentration of formaldehyde in the air using a 95% confidence interval. They can then compare the interval with previous years’ results to see if there are any trends and if there has been a significant change in the amount of formaldehyde in the air.
You work for the EPA and are asked to interpret the results shown in the graph below. The graph shows the point estimate for the population mean concentration and the 95% confidence interval for μ for formaldehyde over a three-year period. The data are based on air samples taken at one city.
3. How do you think the EPA constructed a 95% confidence interval for the population mean concentration of the organic compounds in the air? Do the following to answer the question (you do not need to make any calculations).
A) What sampling distribution do you think they used? Why?
B) Do you think they used the population standard deviation in calculating the margin of error? Why or why not? If not, what could they have used?
According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $ 1,527. (Data extracted from R. A. Smith, ” Fashion Online: Retailers Tackle the Gender Gap,” The Wall Street Journal, March 13, 2008, pp. D1,D10.) Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $ 1,000 for women.
a) State the null and alternative hypothesis if you want to determine whether the mean amount spent is higher for men than for women.
b) In the context of this study, what is the meaning of the Type I error?
c) In the context of this study, what is the meaning of the Type II error?
d) At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women?
1. For each case below, choose the most appropriate statistical procedure:
a. A teacher of a low-level reading group is interested in what the average score is for the group of 25 students.
b. An administrator wants to find out if there is a relationship between teacher absences and student achievement.
c. A math teacher wants to know how many ability groups should be formed within a class of 30 students.
d. A student teacher is interested in finding out the number of students who rate his performance as good, excellent, average, or poor.
2. Identify the scale of measurement in each of the following:
1. attitudes toward school
2. grouping students on the basis of hair color
3. asking judges to rank order students from most cooperative to least cooperative
3. For the following set of scores, prepare a frequency distribution, a histogram, and a stem-and-leaf display for each variable. Also calculate the mean, the median, and the standard deviation of each score. Are there any outliers in the distribution? If so, what is the result if these scores are removed from the data set? Draw a scatter plot that illustrates the relationship between the two variables.
Variable A: Attitude toward descriptive statistics (1 = low and 20 = high) Variable B: Achievement on test of knowledge of descriptive statistics
Sam 12 80
Sally 10 60
Frank 19 85
Bob 8 65
Colleen 2 55
Isaiah 15 75
Felix 1 95
Dan 20 82
Robert 6 70
Jim 11 88
Michelle 3 59
Jan 7 60
To answer Problem 3, use the Excel® Analysis tool where applicable. Using the data from Problem 3 and the Excel® Analysis tool complete the following:
a. Find the following for Variables A and B: mean, median, mode, and standard deviation
b. Create a histogram for Variables A and B and create a scatter gram between Variables A and B
c. Compute the coefficient correlation between Variables A and B
1. How do you plan to use correlation in your example of ethical studies?
2. “Correlation analysis is a mathematical method that allows one to investigate the link, if any exists, between variables and the results, of research. “Key statement is “if any exists”. We can show strong correlations and still there is NO relationship or link between the variables. This is called a spurious correlation and is very common in the real world. Yes, frequency analysis is a tool that can be used to help detect correlations though often running a multivariable correlation is also a quick method for scouting for correlations.
Does a low correlation value of say .4 indicate that there is not a correlation and so should be ignored ?
3. Now what happens when we change the definition of ‘best fit’, then do the values of b0 and b1 change? Why change the definition of best fit?
4. There are several ways common to measuring the volatility (degree of movement or spread) in a sample. Volatility is a common expression.
We are familiar with standard deviation and variance of a sample. However these are often NOT useful when comparing two different samples.
A measure often used when comparing the variation or variability or volatility of two samples is the COEFFICIENT OF VARIATION. The coefficient of variation is the ratio of the standard deviation to the mean of the sample.
Why is this more useful in indicating volatility than just the standard deviation?
Note: the coefficient of variation is often used in stock analysis for indicating volatility.
The Department of Economic and Community Development (DECD) reported that in 2009 the average number of new jobs created per county was 450. The department also provided the following information regarding a sample of 5 counties in 2010.
County New Jobs Created In 2010
Bradley 410
Rhea 480
Marion 407
Grundy 428
Sequatchie 400
a. Compute the sample average and the standard deviation for 2010.
b. We want to determine whether there has been a significant decrease in the average number of jobs created. Provide the null and the alternative hypotheses.
c. Compute the test statistic.
d. Compute the p-value; and at 95% confidence, test the hypotheses. Assume the population is normally distributed.
Chapter review questions attached.
—
1. If it is important to reject a false null hypothesis, the B probability should be:
a. small
b. large
c. close to 1.0
d. negative
e. impossible to tell?
3.. The manufacturer of a refrigerator system for beer kegs produces refrigerators which are supposed to maintain a true mean temperature, of 47 degrees F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and will conduct a hypothesis test to determine whether the true mean temperature differs from this value.
Classify the hypothesis test as two-tailed, right tailed, or left tailed.
a. two-tailed
b. right-tailed
c. left-tailed
4. At one school, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased from the previous mean of 21.6 hours.
Classify the hypothesis test as two-tailed, right tailed, or left tailed.
5. Jenny is conducting a hypothesis test concerning a population mean. The hypotheses are as follows.
H0: = 50
Ha: > 50
She selects a sample and finds that the sample mean is 54.2. She then does some calculations and is able to make the following statement:
If H0were true, the chance that the sample mean would have come out as big ( or bigger) than 54.2 is 0.3. Do you think that she should reject the null hypothesis? Why or why not?
a. No, she should not reject the null hypothesis, the observed sample mean is consistent with the null hypothesis.
b. No, she should not reject the null hypothesis, the observed sample mean is not consistent with the null hypothesis.
c. Yes, she should reject the null hypothesis, the observed sample mean is consistent with the null hypothesis.
d.Yes, she should reject the null hypothesis, the observed sample mean is not consistent with the null hypothesis.
6.
Traditionally in hypothesis testing the null hypothesis represents the “status quo” which will be overturned only if there is evidence against it. Which of the statements below might represent a null hypothesis?
a. the treatment has no effect
b. the defendant is guilty
c. the teaching method raises SAT scores
d. A new brand of battery lasts longer than Brand A batteries
8. A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The hypotheses are:
H0: = 16.1 ounces
Ha: < 16.1 ounces
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean amount of juice is less than 16.1 ounces.
9. In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The hypotheses are:
H0: = 9.4 minutes
Ha: > 9.4 minutes
a.Type I error
b. Type II error
c. Correct Decision
13.
The significance level of a hypothesis test is 0.33. What is the probability of a Type I error? Express your answer as a decimal.
—
(See attached file for full problem description)
** Please see the attached file for the complete problem description **
1) Calculate the mean, mode, median and standard deviation of the means.
2) How does this illustrate the central limit theorem?
3) What is the probability that the mean lies between 5 & 6?
4) What is the 95% confidence interval for the mean?
5) What is the 90% confidence level?
1. Why use the Wilcoxon T test. What is the hypothesis statements you used?
2. Consider do we prefer working with dependent samples or independent samples? Explain
3. We have the statement “The F-ratio provides the ability to determine the deviation between the population and the means and develop a method of accepting or rejecting a hypothesis.” In fact we use the ANOVA which tests variances using the F ratio to determine if the mean values are equal. How can we use a test on variances to tell us about mean values?
4. Do information technology people get the respect they deserve? Ans: Yes.
Examine the question and what are your comments?
5. Consider “ANOVA is important because it gives a person a basis in which to infer if their null and alternative hypotheses are correct or not.” This is true of all statistical testing. What is special about ANOVA?
1. Here are some interesting (and imaginary) facts about cockroaches: The average number of roaches per home in the United States is 57; s = 12. The average number of packages of roach killer purchased per family per year is 4.2; s = 1.1. The correlation between roaches in the home and roach killer bought is .5.
(a) The Cleanly family bought 12 packages of roach killer last year. How many roaches would you predict they have in their home?
(b) The Spic-Spans have 83 roaches at their house. What would be your prediction of how many boxes of roach killer they bought?
Please see attached for full question.
Please see attached for the full details of the problem.
1. (2 pts) The objective of statistics is best described as:
A) To make inferences about a sample based on information we get from a population
B) To make inferences about a population based on information we get from a sample taken from the population
C) To use population mean,  as an estimate of the sample mean,
D) To make inferences about a sample with a high degree of reliability
2. (5 pts) Construct a grouped frequency distribution of the ages that 30 randomly selected smokers started smoking:
25 26 25 17 16 16 14 17 21 16
15 18 17 15 15 19 16 17 23 15
19 17 16 26 16 25 16 17 22 24
3. (2 pts) Three-fourths of the numbers in any data set will be larger than the
A) first quartile B) third quartile C) median D) midrange E) fourth quartile
4. (2 pts) The number that appears most frequently in a data set is the
A) mean B) midrange C) median D) mode E) average
5. (2 pts) Half of the scores in any data set are below the
A) first quartile B) midrange C) third quartile D) median E) fourth quartile
6. (6 pts) Find the mean, median, and mode for the following set of data which shows the number of pages per article in a random sample of magazine articles.
6 7 5 4 7 5 5 7
8 5 3 6 8 9 5
7. (8 pts) Construct a histogram and a frequency polygon for the following frequency distribution
Miles Number of Commuters
Class Frequency
0 – 20 7
21 – 40 3
41 – 60 12
61 – 80 10
81 -100 4
8. (5 pts) State True or False
a) A collection of all the objects to be studied is a population.
b) A subset or part of the population is called a partial population.
c) In a frequency distribution, the class size is always 4.
d) The sum of the percents of the sectors in a pie chart should be 100%.
e) A frequency distribution can be illustrated using a histogram.
9. (6 pts) In a study of 100 married women with children, the subjects were asked the major reason for working outside the home. The study resulted in the following data:
Reason Number of Responses
To support self/family 65
For extra money 20
For something different to do 10
Other 5
—————————————————————-
Total 100
Construct a pie chart for the data and analyze the results.
10. (2 pts) A county commissioner would like to find out how people in his county feel about a county lottery to support education. How might a cluster sample be selected?
11. (4 pts) The following statistics provide information about the scores on a national History exam.
Mean 540 First Quartile 260
Median 450 Third Quartile 678
Mode 468 90th Percentile 890
a) What score did half of the test takers surpass?
b) What was the most common score?
c) What percentage of the test takers scored 678 or better?
d) If Joe had a score of 890, explain the meaning of his score.
Consider an example of 100 executives………
1. Why use statistics in business research, and what is its role?
2. How can the concept of variance and standard deviation be applied to solving a real world business-related problem? Include a specific example from business. Explain.
3. When would you use descriptive statistics over inferential statistics? Give a specific scenario and explain your rationale.
4. Why is using Baye’s theorem (conditional probabilities) important to help answer business-related questions? What does this theorem allow you to do?
6. In 1978, a small plane slammed into a passenger jet over San Diego, killing 144 people. Langhorne Bond, then the head of the FAA, responded by proposing strict new curbs on small planes around many busy airports.
Examine the following FAA data. Is there a statistically significant difference in the frequency of different types of near midair collisions between the first 6 months of 1985 and the first 6 months of 1986? A corporate plane in this case, means a UPS or FEDEX type of aircraft.
Type of Incident Jan-July ’85 Jan-July ’86
O E O E
2 airliners 15 16.6 19 17.4
1 airliner and
1 corporate plane 99 112 130 117
2 corporate planes 262 247.4 244 258.6
TOTAL 376 393
Use Chi-square to solve question 6
7. The following data represents a study of a main street in your town USA. The city monitored speeds on main-street before a stop light was installed. They then conducted a study after a stop light was installed to see if there was an effect on the speed of the cars cruising down main-street. At 95% level of confidence.
Direction Before the Stop Light After Stop Light
9 am Westbound 32.1 32.2
9 am eastbound 32.2 32.9
1 pm westbound 32.6 32.4
1 pm eastbound 33 31
8 pm westbound 31.2 31.4
8 pm eastbound 33.5 31.6
Use T-test for paired data to solve question 7
8. Calculate the following at a .05 level of significance:
Population 1 Population 2
Sample size n1 = 30 n2 = 35
Sample mean xbar1 = 22.3 xbar2 = 18.5
Sample st. dev s1 = 1.5 s2 = 2.2
Use Z-test for unpaired data to solve question 8
DATA:
Day 1: 45 mins.
Day 2: 37 mins.
Day 3: 49 mins.
Day 4: 53 mins.
Day 5: 41 mins
Day 6: 43 mins
Day 7: 31 mins.
Day 8: 46 mins.
Day 9: 39 mins.
Day 10: 43 mins
Day 11: 47 mins
Day 12: 39 mins
Day 13: 53 mins
Day 14: 42 mins
Day 15: 39 mins
1. Divide your data in half, your first 8 observations and your last 7 observations. Then use ANOVA to test to see if there is a significant difference between the two halves of your data.
2. Take your data and arrange it in the order you collected it. Count the total number of observations you have, and label this number N. Then create another set of data starting from one and increasing by one until you reach N. For example, if you have 10 observations, then your new set of data would be (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). This set of data is called a time series. Run a regression using your original set of data as your dependent variable, and your time series as an independent variable.
Use the following table when answering Questions 44 – 48:
Data Indicates You Should: The Actual Situation:
H0 is True HA is True
Believe H0
Believe HA A
C B
D
44. The correct missing description of the conditions defined by cell A is
a. Type I error committed.
b. Type II error committed.
c. you correctly believe a true null hypothesis.
d. you correctly reject the null hypothesis.
e. None of the above
45. The correct missing description of the conditions defined by cell B is
a. Type I error committed.
b. Type II error committed.
c. you correctly believe a true null hypothesis.
d. you correctly reject the null hypothesis.
e. None of the above
46. The correct missing description of the conditions defined by cell C is
a. Type I error committed.
b. Type II error committed.
c. you correctly believe a true null hypothesis.
d. you correctly reject the null hypothesis.
e. None of the above
47. The correct missing description of the conditions defined by cell D is
a. Type I error committed.
b. Type II error committed.
c. you correctly believe a true null hypothesis.
d. you correctly reject the null hypothesis.
e. None of the above
48. As the probability of making a Type I error increases
a.  decreases.
b.  increases.
c.  +  increases
d. Nothing will change
e.  decreases
See attached file for full problem description.
Payne (2001) gave participants a computerized task in which they first see a face and then a picture of either a gun or a too. The task was to press one button if it was a tool and a different one if it was a gun. Unknown to the participants while they were doing the study, the faces served as a “prime” (something that starts you thinking a particular way) and half the time was of a black person and half the time of a white person. Table 2-8 shows the means and standard deviations for reaction times (time to decide if the picture is of a gun or a tool) after either a black or white prime. (In Experiment 2, participants were told to decided as fast as possible.) Explain the results to a peson who was never had a course in statistics. (Be sure to explain some specific numbers as well as the general principle of the mean and standard deviation.)
Table 2-8 Mean Reaction Times (in Milliseconds) in Identifying Guns and Tools in Experiments 1 and 2
Prime
Black White
Experiment 1 M SD M SD
? Gun 423 64 441 73
? Tool 454 57 446 60
Experiment 2
? Gun 299 28 295 31
? Tool 307 29 304 29
1. An appropriate 95% confidence interval for mu has been calculated as (- 0.73, 1.92) based on n = 15 observations from a population with a normal distribution. The hypotheses of interest are H0 : mu = 0 versus Ha: mu <> 0. Based on this confidence interval …
3. An analyst, using a random sample of n = 500 families, obtained a 90 percent confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used a 99 percent confidence coefficient instead, the confidence interval would be …
4. A Gallup poll of a sample of 1089 Canadians (total population of 26,000,000) found that about 80% favored capital punishment. A Gallup poll of a sample of 1089 Americans (total population of 260,000,000) also found that 80% favored capital punishment. Which if the following statements is TRUE?
5. A 95% confidence interval for mu is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H0 : mu = 0 vs HA:mu <> 0 at the alpha = 0.05 level, using the same data as was used to construct the c.i …
6. In a statistical test for the equality of a mean, such as H0 : mu = 10, if alpha = 0.05, then …
7. In hypothesis testing, beta is the probability of committing an error of Type II. The power of the test, 1 − beta is then …
8. Resting pulse rate is an important measure of the fitness of a person’s cardiovascular system with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled was selected and the mean pulse resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. A possible Type II error would be to:
9. During the pre-flight check, Pilot Jones discovers a minor problem – a warning light indicates that the fuel gauge may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be the appropriate null hypothesis? The type I error?
10. The average time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let mu denote the average time to obtain pain relief with the new product. An experiment is conducted to verify if the new product is better. What are the null and alternative hypotheses?
11. The sample mean is an unbiased estimator for the population mean. This means:
12. What is a statistical inference?
13. Does playing music to dairy cattle increase their milk production? An experiment was conducted where a group of dairy cattle was divided into two groups. Music was played to one group; the control group did not have music played. The average increase in production was 2.5 l/cow over the time period in question. A 95% confidence interval for the difference (treatment-control) in the mean production was computed to be (1.5,3.5) l/cow. This means:
A professional auto racing driver was given training in competition driving techniques. His driving times in seconds on five different race tracks were recorded before and after the training. At the 0.01 level of significance, was the training beneficial? State and conduct an appropriate hypothesis test.
Track Before Training After Training
1 226 198
2 706 701
3 559 589
4 975 892
5 280 264
The owner of a Tucson, Arizona sports bar wants to determine if University of Arizona (U of A) college football games on Saturdays are more popular than Arizona Cardinals professional football games on Sunday. He obtained A.C. Neilson data for a recent fall football weekend. On Saturday, 140 households out of 400 contacted were watching the U of A game. On Sunday, 150 households out of 600 contacted were watching the Arizona Cardinals game. At the 5% level of significance, what should he conclude? State and conduct an appropriate hypothesis test.
Discuss the Statistics questions below.
1. Very good list of characteristics of good business research. Quite a detailed list for each:
A. Good business research presents opportunities, outweighed by potential risks or costs of conducting the research, that enable the organization to grow and develop new strategies to improve and enhance business practices, processes, and performance.
B. Good business research allows companies to discover information, otherwise unattainable, which is aligned with business goals, plans, and objectives, provides clarity in direction that can be applied logical and realistically implemented with good business decisions
C. Good research meets the following criteria completely, is lucrative and worthwhile, and presents benefits that surpass the costs, efforts, and time necessary to conduct it effectively.
D. Good research uses diversified data collection methods to ensure accuracy and completely depictions of the population are represented through collection methods aligned appropriately with the research model best suited for the project.
E. Good research is cost effective, in terms of the value of the information and the methods for conducting the research.
F. Good research is not influenced by stereotypes, suspicions, skewed researchers, and assumptions.
G. It enables the company to gain more in value than the costs associated with conducting the research, by presenting numerous benefits, opportunities, and supporting organizational health and success.
H. Solid (good) research practices employ observation, hypothesis, prediction, and testing to help organizations innovatively meet demands, solve problems, and remain competitive.
This is quite a detailed list of characteristics of good business research. I will hypothesize that if a research meets all the 8 characteristics, it is probably good research. So let us assume these are sufficient conditions for good business research.
Now which (if any) of the conditions are necessary to have good research? For example is #5, cost effective, necessary for good research? Often the best way to research something is only found after the first research finds a way.
2. A question which has arisen in our discussion and you to think about concerns, can a research be consider good research if the conclusions are correct but:
a) Management takes no action?
b) Management takes the wrong action?
3. Consider, your example, “The weight of the average has to do with overall customer accounts and takes error into consideration. Without confidence intervals, the data may be inconsistent, exaggerated, or inaccurate. ” good.
Now why does having a confidence interval, CI, answer ” Without confidence intervals, the data may be inconsistent, exaggerated, or inaccurate ” ?
4. Consider, “We anticipate a growth rate of about 5-7% per year, and for the past 3 years we nearly doubled our expected forecasts so we are on the right track of success within our business. “
Think about an example, You have hired a consultant.
a)He is consistently forecasting the range of sales growth (confidence interval of 95%) to be 5 to 7%.
b) we are actually seeing sales growth of 10 to 14%.
Care to comment?
5. It. is not easy to assure a random sample or that the sample is from the correct frame. Errors can occur accidentally with the best of intentions. Some classic examples of where the intent is to get random representative samples but the result are not successful. Here are some examples:
â?¢Doing a telephone survey (telephone book or lists) for voter preferences. (this is cited as one reason the polls declared Dewey won when Truman actually one in 1948)â?¢Survey every third customer in the mall in the morning â?¢Internet surveys
Why are these three examples NOT random?
The following data are the grade point averages x and the monthly salaries y for students who had obtained a bachelor’s degree in business administration with a major in information systems. The estimated regression equation for these data is y^ = 1790.5 + 581.1x
(See attachment for full question)
1. a. Why is “level of measurement” important,
b. What is level of measurement, and
c. Why is the level important?
2. What is necessary for the temperature measurement to be called Interval?
Is there a way to use the temperature measurement so it is a Ratio level?
3. What are the requirements to prove causality?
4. We talk about sampling and questionnaires. Let us look at background and do some reflection and investigation into what will help us in practice. How is the data collected? There is a whole series of questions we use to sort through the data. Generally there are four typical means of collecting data: surveys, focus groups, observational studies, and data mining. The data collected may be primary or secondary data sources. When planning to collect data the questions fall into three general types: administrative, target and classification. Even when collecting secondary data we end up asking these three types of questions because we organize our results along these lines. Administrative questions are for general information. Target questions involve the specific information pertinent to the research question. Classification questions are exactly that. Unfortunately, all methods of data collection are subject to error, bias, abuse, and misuse. This is another reason for vigilance in determining design validity, measurement validity and reliability, and ethics.
When considering the ethical implications of research there are six major groups that must be considered. The groups are: the participant, the researcher, management, the business, and society. Each group has expectations and rights and each group owes others certain rights. There is considerable information available and discussion on the rights of each group. In summary, each expects (should demand): privacy, honesty, objectivity choice, safety, informed, and respect. In practice, unethical behavior negatively affects every area of business. Most organization and business groups have established and publish codes of conduct (ethical standards).
Any comments on how effective is self-policing of organizations for ethical impropriety?
Performance/Sector BioTech IT
Positive 23% 17%
Negative 7% 53%
The table above displays data on the composition and performance of the Massachusetts Bubble Growth (MBG) technology stock fund over the last year. The table includes data on the distribution of stocks in the fund by technology sector (information technology (IT) or biotechnology) and by last year’s “performance” (positive or negative net change in share price over the last year).
What is the conditional probability that an MBG stock had a positive change in share price, given that it is an IT stock?
Source
24.3%
42.5%
40.0%
None of the above
See the attached file.
Question 1: (please help me in question 1.2 to 1.5.3 and please do check 1.1, if it is correct or not)
(i) A production manager at a firm recorded the outputs of the all workers in the production division during a certain shift and obtained the following results.
1496 1377 1336 1103 1284 1459 1401 1535
1519 1390 1355 1228 1329 1484 1440 1674
1505 1385 1339 1162 1310 1462 1401 1568
1517 1388 1347 1227 1322 1483 1406 1605
1526 1392 1362 1232 1335 1491 1443 1693
1.1 Use the stem and leaf method to construct a grouped frequency distribution of the above data.
Use a total of six classes and let 1100 units be the lower limit of the smallest class. (5)
Solution:
Frequency Stem Leaf
2 11| 03 62
4 12 | 27 28 32 84
14 13| 10 22 29 35 36 39 47 55 62 77 85 88 90 92
11 14| 01 01 06 40 43 59 62 83 84 91 96
6 15| 05 17 19 26 35 68
3 16 | 05 74 93
Key: 16|05 means 1605.
Frequency distribution is shown below in the table
Class Frequency
1100-1199 2
1200-1299 4
1300-1399 14
1400-1499 11
1500-1599 6
1600-1699 3
1.2 Use the grouped data of 1.1 to determine the mean, median and modal outputs. Interpret you results.
1.3 Draw to scale the cumulative frequency polygon for the above data.
1.4 Use the cumulative frequency polygon to estimate the interquartile range. Interpret the result you obtained.
1.5 Calculate the 70th percentile using:
1.5.1 the raw data given in the table above.
1.5.2 the grouped frequency distribution.
1.5.3 the less than cumulative polygon.
I simply need help with setting up the formula or an example of how to complete the problem on my own. I have been reading the topics but nothing explained what formula to use to get the answer so can someone please show me the steps so I can compute it myself.
1.) The distribution of weights for a sample of 1,400 cargo containers is somewhat normal. Based on the Empirical Rule, what percent of weights will be A.) Between the mean and plus or minus twice the standard deviation, B.) Between teh mean and minus one standard deviation, and C.) Between the mean and three standard deviation
2.) Dan Woodard is the owner and manager of Dan’s Truck Stop. Dan offers free refills on all coffee orders. He gathered the following information on coffee refills: there is a 30% chance that a customer will not get a refill, a 40% chance that a customer will get one refill, a 20% chance that a customer will get two refills, and a 10% chance that a customer will get three refills. How many refills can Dan expect a customer to get?
3.) WNAE finds that the distribution fo the length of time listeners are tuned to the station is normal, with a mean of 15 minutes and a standard deviation of 3.5 minutes. What is the probability that a particular listener will tune for. A.) More than 20 minutes
B.) For 20 minutes, or less
C.) Between, 10 and 12 minutes
4.) The monthly sales of muffles in Richmond, VA area follow a normal distribution, with a mean of 1,200 and a standard deviation of 225. The manufacturer want to establish inventory levels such that there is no more than a 5% chance of running out of stock. What level should the manufacturer select as the minimum inventory level?
1. Consider your example, “For instance, if we want to compare student grades of public universities to private universities, we would look at independent grade samples of public universities and private universities – yes, or we could create dependent grade samples from the public versus the private university.
It is not the initial population that determines if the final samples are dependent or independent. The initial samples can come from the same population and our final samples be either independent or dependent.
For example, consider the population of realtors a Sample A is 10 public universities. Sample B is 13 public universities. We have standardized test ZZZ with 42 questions to give to each school.
Please explain:
a) How do we Test the mean difference in scores for public versus private universities (as independent samples)
b) How do we test the mean difference in scores for public versus private universities (as dependent samples?)
2. If we are testing the mean running time on 100 yards of a group of 10 parents versus the mean running time of a group of 10 of their children, the samples are independent if we test the mean time of parent group versus mean time of the children group. What is necessary to make the samples dependent?
Repeat for the “before, after”, “inches of rain, tree growth”
3. Consider the survey question:
Do information technology people get the respect they deserve? Ans: Yes or No.
Examine the question and what are your comments?
4. Now why must a STOH always have a null and an alternative hypothesis?
* Please see attachment*
i am submitting a complex lengthy stats problem, with accompanying excel file. I am beginning stats student. I am more interested in theoretical explanations to help me to learn the problem. I am also interested in basic level internet references to help me to understand material. It is irrelevant whether or not you provide correct answer, so long as you have provided detailed logical explanations that will help me to learn.
Please keep in mind that this is my first stats class, and this is foreign to me. I have basic literacy in excel.
thanks
———————————————-
Kilgore Manufacturing, Inc. (KMI) is a small manufacturing company in the St. Louis area that produces components used in the aerospace industry. James Kilgore, the president and owner of KMI, started the company five years ago. Although business has been reasonably steady for the last two years, KMI has yet to establish any long-term relationships with major aerospace contractors. This is important, because small companies like KMI only get business as subcontractors to the large aerospace manufacturing companies that win major contracts, many of which are with the federal government.
[see attachment for remainder of text]
The data for the first 60 days of production under the new manufacturing process implemented at KMI is collected and available for our analysis. This database contains
1. month of production day,
2. date of the month for that production day, and
3. number of units produced on that day.
Please answer the following questions based on the above data and the data provided in the Kilgore.xls file.
1. Calculate the guaranteed minimum daily production level under the existing production process that will result in an average net daily profit of $1,000, the amount needed by KMI. Show all your work.
2. On what percentage of production days will KMI incur a penalty if they bid this number of units? Show all your work.
3. Analyze the distribution of daily production levels under the new production process suggested by one of the workers. How does it compare to the existing method? What are the characteristics of its distribution? Is normal distribution appropriate for it?
4. Do the data support Bill Shelton’s claim of quick learning process for the new production process? How does it affect your approach to the analysis of these data?
5. Under the new production process, what guaranteed minimum daily production level would you recommend that KMI propose in their bid? Explain your answer and show your work. Support any assumptions with evidence from the data analysis where possible.
1. What is it that specifically we can do (and do) when we develop regression equation? We are using …………….. to forecast the dependent variable. We get the relationship how?
What if we are using regression to predict retail sales based on ……………………………….. How do we go about analyzing the changes in the data …
2. . Consider your example, “sales generated by making calls from a â??qualified leads listâ?, an educated assumption can be made to determine the level of sales generated based on calls made. This will allow staffing levels and realistic goals to be set. ” Let us set up the problem: Assume basic form: y = b0 + b1x
x= independent variable = sales generated
y= dependent variable = ?
Let us assume sales generated is in dollar amounts sold (it could be just the number of sales).
a- what type of relationship do we expect?
b- how will we determine the”This will allow staffing levels and realistic goals to be set. “
3. What are the necessary conditions (assumptions) that are needed if:
a- the regression analysis is to produce an answer for us? and
b- for the linear regression to be valid and successful? and
c- The statistical implications of we use in analyzing linear regression are to be valid?
1. Determine if this is an example of probability or statistics:
Of 100 coin tosses, 50 are likely to be “heads”.
2. Determine if this data is qualitative or quantitative:
State of residence
3. Determine if this study is experimental or observational:
A survey asks which candidate registered voters prefer. (Points :3)
4. Construct a frequency distribution for the data given below…
5. Determine if this is an example of a variable or a parameter:
Weight
6. Determine if this statistical study is descriptive or inferential:
A study establishes a link between obesity and heart disease…
7. Given the following histogram, create a grouped frequency distribution…
8. Identify the sampling technique used to obtain this sample:
A CDC official selects the first ten US hospitals in an alphabetical listing, and asks them how many flu cases they’ve seen in the last year…
9. Identify the sampling technique used to obtain this sample:
As a group of citizens enter a courthouse, a bailiff selects each 5th person for jury duty…
(See attached file).
1. Find the indicated critical z value.
Find the value of zα/2 that corresponds to a confidence level of 97.80%.
2. Find the appropriate minimum sample size.
You want to be 95% confident that the sample variance is within 20% of the population variance.
4. Express the confidence interval using the indicated format.
Express the confidence interval 0.457 ± 0.044 in the form of P^ – E < p < P^ + E
4. Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.
The duration of telephone calls directed by a local telephone company: σ=3.6minutes, n=560, 90%confindence Round your answer to the nearest thousandth.
5. Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
A company produces refrigerators for beer kegs. The refrigerators are supposed to maintain a mean temperature of 43°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the company and claims that the mean temperature is incorrect. Identify the type II error for the test.
a. Fail to reject the claim that the mean temperature is equal to 43°F when it is actually 43°F.
b. Reject the claim that the mean temperature is equal to 43°F when it is actually different from 43°F.
c. Fail to reject the claim that the mean temperature is equal to 43°F when it is actually different from 43°F.
d. Reject the claim that the mean temperature is equal to 43°F when it is actually 43°F.
6. Find the critical value or values of χ2 based on the given information.
H1: σ > 3.5
n = 14
α = 0.05
7. Find the critical value or values of χ2 based on the given information.
H1: σ ≠ 9.3
n = 28
α = 0.05
8. Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test of the claim h
as been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
a. There is sufficient evidence to support the claim that the standard deviation is different from 3.3 mg
b. There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg.
c. There is sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg
d. There is not sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg/
9. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter.
A researcher claims that 62% of voters favor gun control.
a. H0: p < 0.62
H1: p ≥ 0.62
b. H0: p = 0.62
H1: p ≠ 0.62
c. H0: p ≠ 0.62
H1: p = 0.62
d. H0: p ≥ 0.62
H1: p < 0.62
5. A product manager at Proctor & Gamble seeks to determine whether her company should market a new brand of toothpaste, called Tim’s of Massachusetts. If the new brand succeeds, then P&G estimates that it would earn $2,000,000 in NPV. If Tim’s fails, then the company expects to lose approximately $800,000 in NPV. If P&G decides not to market this new brand, the product manager believe there would be little, if any, impact on the profits earned through sales of P&G’s other products. The manager has estimated that the new brand has a 40% chance of succeeding. Before making her decision, the manager can decide to spend $75,000 on a market research study. Such a study of consumer of consumer preferences will yield either a positive recommendation with probability 0.50 or a negative recommendation with probability 0.50. A positive recommendation by the market research study will indicate that the probability of success for Tim’s is 70%; whereas a negative recommendation will indicate that the probability of success for Tim’s is 20%.
a) Construct a decision tree of the product manager’s decision.
b) Calculate the EMV of the two alternatives and identify the course of action that maximizes EMV.
c) The product manager though it prudent to run a sensitivity analysis on 5 variables:
 The probability of success
 Success Profit
 Failure Profit
 Prob of success if market research indicates launch, and
 Prob of success if market research indicates not to launch.
The following shows the tornado diagram and two of the five sensitivity graphs. What conclusions can you draw from each of these graphs? State a sentence or two for each graph below.
6. Nicklaus Electronics manufactures electronic components used in the computer and space industries. The following analysis is based on the annual rate of return on the market portfolio and the annual rate of return on Nicklaus Electronics stock for the last 36 months. The company wants to calculate the “systematic risk” of its common stock. (It is systematic in the sense that it represents the part of the risk that Nicklaus shares with the market as a whole.) The rate of return Yt in period t on a security is hypothesized to be related to the rate of return mt on a market portfolio by the equation
Yt = a + bmt + et
Here, a is the risk-free rate of return, b is the security’s systematic risk, and et is an error term.
a) Using the output below, estimate the systematic risk of the common stock of Nicklaus Electronics.
b) Would you say that Nicklaus stock is a “risky” investment? Why or why not?
Results of multiple regression for Stock_Return
Summary measures
Multiple R 0.8045
R-Square 0.6473
Adj R-Square 0.6369
StErr of Est 0.0549
ANOVA Table
Source df SS MS F p-value
Explained 1 0.1878 0.1878 62.3944 0.0000
Unexplained 34 0.1023 0.0030
Regression coefficients
Coefficient Std Err t-value p-value
Constant 0.0221 0.0197 1.1242 0.2688
Market_Return 1.4328 0.1814 7.8990 0.0000
4. State the steps that you should follow when conducting a regression analysis.
5. What is a residual in a regression analysis?
6. How many residuals are there in a regression analysis?
7. What information can you discover when analyzing residuals?
(1) Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 500 steady smokers revealed that the sample mean is $30 and the sample standard deviation is $8.00. What is the point estimate of the population variance?
(a) 30
(b) 40
(c) 8
(d) 64
(e) None of the above __________
(2) For a given level of confidence and sample size, what will happen to the confidence interval for the population mean as the population variance decreases?
(a) Remains the same
(b) Gets narrower
(c) Gets larger
(d) Cannot be determined
(e) None of the above __________
(3) Which statement is incorrect regarding the Student’s t-distribution?
(a) Mean = 0
(b) Symmetric distribution
(c) Based on degrees of freedom
(d) There is only one distribution
(e) All of the above are correct __________
(4)The mean number of travel days per year for the outside salespeople employed by hardware distributors is to be estimated. The 0.90 degree of confidence is to be used. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If the population mean is to be estimated within two days, how many outside salespeople should be sampled?
(a) 134
(b) 452
(c) 511
(d) 1069
(e) None of the above
__________
(5) The claim that “40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available” is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?
(a) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58
(b) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.33
(c) Reject the null hypothesis because 37% is less than 40%
(d) Do not reject the null hypothesis because 37% lies in the area between 0 and 40%
(e) None of the above __________
(6) Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are below regular, regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades. Assuming any grade can be used at the 0.05 level, what is the critical value of F?
Kilometers per liter
Below Super
Trial # Regular Regular Premium Premium
1 39.31 36.69 38.99 40.04
2 39.87 40.00 40.02 39.89
3 39.87 41.01 39.99 39.93
(a) 1.96
(b) 2.33
(c) 4.07
(d) 12.00
(e) None of the above is correct __________
A researcher measures the following scores for a group of people. The X variable is the number of errors on a math test, and the Y variable is the person’s level of satisfaction with his/her performance.
A.) With such ratio scores, what should the researcher conclude about this relationship?
B.) How well will he be able to predict satisfaction scores using this relationship?
Participant Errors X Satisfaction Y
1 9 3
2 8 2
3 4 8
4 6 5
5 7 4
6 10 2
7 5 7
17.1 Life tests on a sample of five units were conducted to evaluate a component design
before release to production. The units failed at the following times:
Unit Failure Time,
Number hours
1 1200
2 1900
3 2800
4 3500
5 4500
Suppose that the component was guaranteed to last 1000 hours. Any failures during this
period must be replaced by the manufacturer at a cost of $200 for each component.
Although the number of test data is small, management wants an estimate of the cost
of replacements. If 4000 of these components are sold, provide a dollar estimate of
the replacement cost.
What is the sampling distribution of sample means?
What is the mean of the sampling distribution of sample means?
What is its standard deviation?
How is that standard deviation affected by the sample size?
What does the central limit theorem state about that distribution?
1
Kim Davis has decided to purchase a cellular phone, but she is unsure about which rate plan to select. The “regular plan” charges a fixed fee of $55 per month for 1000 minutes of airtime plus $0.33 per minute for any time over 1,000 minutes. The “executive plan” charges a fixed fee of $100 per month for 1,200 minutes of airtime plus $0.25 per minute over 1,200 minutes.
A) If Kim expects to use the phone for 21 hours per month, which plan should she select?
B) At what level of use would kim be indifferent between the two plans?
Instructions In all exercises, include MegaStat, Excel, or MINITAB exhibits to support your calculations. State the hypotheses, show how the degrees of freedom are calculated, find the critical value of chi-square from Appendix E or from Excel’s function =CHIINV(alpha, deg_freedom), and interpret the p-value. Tell whether the conclusion is sensitive to the level of significance chosen, identify cells that contribute the most to the chi-square test statistic, and check for small expected frequencies. If necessary, you can calculate the p-value by using Excel’s function =CHIDIST(test statistic, deg_freedom). Note: Exercises marked * are harder or require optional material.
15.18- Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned? Certainty
Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
0-9 12 8 3 23
10-59 8 4 10 22
60 or more 1 7 11 19
Col Total 21 19 24 64
15.22- A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary by mall location? (Data are from a project by MBA students Steve Bennett, Alicia Morais, Steve Olson, and Greg Corda.) Vehicles
Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total
Car 44 49 36 64 193
Minivan 21 15 18 13 67
Full-Sized Van 2 3 3 2 10
SUV 19 27 26 12 84
Truck 14 6 17 9 46
Col Total 100 100 100 100 400
15.24- High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels), or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase? (Data are from Capt. Robert E. Hartl, retired.) Noise
Noise Level Climb Cruise Descent Row Total
Low 6 2 6 14
Medium 18 3 8 29
High 1 3 14 18
Col Total 25 8 28 61
15.28- Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2) and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.) Cola
Correct? Regular Cola Diet Cola Row Total
Yes, got it right 7 7 14
No, got it wrong 12 20 32
Col Total 19 27 46
A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled ‘3 pounds’. Of course, he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.
a. What is the estimated population mean?
b. Determine a 95 percent confidence interval for the population mean.
Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study,
researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age
58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the
inactive pill. (a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value. Interpret
Doane−Seward: Applied
Statistics in Business and
Economics
10. Two−Sample
Hypothesis Tests
Chapter 10 Two-Sample Hypothesis Tests 431
the results at α = .01. (c) Is normality assured? (d) Is the difference large enough to be important?
(e) What else would medical researchers need to know before prescribing this drug widely?
A) What is the response variable and what is the factor?
b) Ho many levels of the factor are being studied?
c) Is there any difference in the average time to failure of the disks from the 3 different suppliers? If so, which ones are different?
d) What is your recommendation to the company and why?
See attached
A final exam in sociology has a mean of 72 and a standard deviation of 9.2….
The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025?
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance,is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.
2.1 Calculate the most appropriate measures of central tendency for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms.
A. GNDR
B. TRAK
C. ADV
D. GPA
2.2 Calculate the most appropriate measures of dispersion for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms.
A. TRAK
B. LIKE
C. STDY
D. GPA
[See the attached questions file.]
Explain the difference between the null hypothesis and the alternate hypothesis. How is the null hypothesis chosen (why is it null)? What is the importance of rejecting the null hypothesis in relation of the sample to the population? With a failure to reject the null hypothesis, can we make a general statement about the population based on the sample findings?
1. A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor. Based on this sample, what is the initial hunch? Would one claim with 95% confidence that the mayor will win a majority of the votes? Explain.
2. As a sample size approaches infinity, how does the student’s t distribution compare to the normal z distribution? When a researcher draws a sample from a normal distribution, what can one conclude about the sample distribution? Explain.
Solve this by using Appendix B.1 table
Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.
a.) What fraction of the employees cost more than $1,500 per year for dental expenses?
b.) What fraction of the employees cost between $1,500 and $2,000 per year?
c.) Estimate the percent that did not have any dental expense.
d.) What was the cost for the 10 percent of employees who incurred the highest dental expense?
Explain the difference between a left tail, two-tailed, and right tailed text. When would we choose a two tailed test? How can we tell the direction by looking at a pair of hypothesis? How can we tell which direction (or no direction) to make the hypothesis by looking at the problem statement (research question)?
Why is population shape of concern when estimating a mean? What does sample size have to do with it?
A union of restaurant and foodservice workers would like to estimate the mean hourly wage,(m), of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate (m) using the mean of the sample. What is the minimum sample size needed in order for the union to be 99% confident that its estimate is within $0.45 of (m)? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.25 . (m)= the greek letter “mu”) is used to denote the population mean.
Question 1:
Find the number of successes x suggested by the given statement.
Among 680 adults selected randomly from among the residents of one town, 27.2% said that they favor stronger gun-control laws.
a. 183
b. 184
c. 186
d. 185
Solve the problem.
In a game, you have a 1/29 probability of winning $106 and a 28/29 probability of losing $9 What is your expected value?
a. $3.66
b. $12.34
c. -$5.03
d. -$8.69
Solve the problem.
The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 99 inches, and a standard deviation of 14 inches. What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 101.8 inches?
a. 0.4192
b. 0.9192
c. 0.0808
d. 0.5808
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution.
The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:
6 15 5 11 11
5 7 9 15 11
Find a 95 percent confidence interval for the population standard deviation σ.
a. (2.6, 6.8)
b. (2.5, 6.2)
c. (0.8, 2.4)
d. (2.6, 6.2)
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution.
College students’ annual earnings: 98% confidence; n = 9, x = $3211, s = $897
a. $545 < σ < $1755
b. $706 < σ < $1170
c. $606 < σ < $1718
d. $566 < σ < $1978
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use ά 0.05.
a. Reject null hypothesis. There is sufficient evidence to support the claim that the proportion with lawn mowers in Omaha is 0.64.
b. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the proportion with lawn mowers in Omaha is 0.64.
c. Reject null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion with lawn mowers in Omaha is 0.64.
d. Fail to reject null hypothesis. There is not sufficient evidence to support the claim that the proportion with lawn mowers in Omaha is 0.64.
Find the indicated probability.
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.
a. 0.7733
b. 0.7744
c. 0.176
d. 0.0144
Construct the indicated confidence interval for the difference between population proportions p1 – p2. Assume that the samples are independent and that they have been randomly selected.
In a random sample of 300 women, 50% favored stricter gun control legislation. In a random sample of 200 men, 30% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 – p2.
a. 0.088 < p1 – p2 < 0.312
b. 0.099 < p1 – p2 < 0.301
c. 0.115 < p1 – p2 < 0.285
d. 0.111 < p1 – p2 < 0.289
Exercise 1
One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150 clamps, the average time needed to complete this step was 72 seconds and the standard deviation was 10 seconds.
(a) Find the probability that the average time to complete the step is between 65 and 74 seconds (inclusive).
(b) Find a 93% confidence interval for the mean time needed to complete the step.
(c) What is the confidence level of the interval (71, 73)?
(d) How many clamps must be sampled so that a 88% confidence interval specifies the mean to within +-1.5 seconds?
(e) Find a 97% lower confidence bound for the mean time to complete the step.
Exercise 2
A new concrete mix is being designed to provide adequate compressive strength for concrete blocks. The specification for a particular application calls for the blocks to have a mean compressive strength greater than 1350 kPa. A sample of 100 blocks is produced and tested. Their mean compressive strength is 1356 kPa and their standard deviation is 70 kPa.
a) Do you believe it is plausible that the blocks do not meet the specification, or are you convinced that they do? Explain your
reasoning by carrying out the appropriate hypothesis test.
b) If a sample of 10 blocks is produced and tested with their mean compressive strength at 1372 kPa and their standard deviation at 68 kPa. Find the P-value based on the same hypothesis.
Exercise 3
A particular type of gasoline is supposed to have a mean octane rating of 90%. Five measurements are taken of the octane rating and the results (in %) are 87.0, 86.0, 86.5, 88.0, 85.3.
a) Test the requirements of the octane rating using the appropriate hypothesis test (assume alpha = 0.01).
b) Verify your result in part (a) using the appropriate confidence interval.
Question 44: (2 points)
A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram to answer the question. The blood pressure readings were given to the nearest whole number.
* pic attached
Identify the center of the third class.
a. 125
b. 120
c. 130
d. 124
Question 46: (2 points)
Determine whether the given value is a statistic or a parameter.
After taking the first exam, 15 of the students dropped the class.
a. Parameter
b. Statistic
Perform the indicated goodness-of-fit test.
Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively.
Response A B C D E
Frequency 12 15 16 18 19
a. Reject the null hypothesis. There is sufficient evidence to support the claim that the responses occur according to the stated percentages.
b. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
c. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the responses occur according to the stated percentages.
d. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the responses occur according to the stated percentages.
‘
Find the original data from the stem-and-leaf plot.
Stem Leaves
————
7.4 1 8
7.5 8 9
7.6 1 9 9
a. 7.41, 7.48, 7.58, 7.59, 7.61, 7.69, 7.69
b. 0.84, 0.84. 1.55, 1.55, 1.65, 0.86, 1.66, 1.67
c. 7.41, 7.42, 7.58, 7.59, 7.65, 7.69, 7.69
d. 0.84, 1.54, 1.55, 1.65, 0.86, 1.66, 1.66
Find the value of the chi-square test statistic for the goodness-of-fit test.
According to recent research, the distribution of the number of children per family in the U.S. is as follows:
Number of children Percent
——————————–
More than 3 20.3
3 21.3
2 14.5
1 16.1
0 27.8
A random sample of 700 families with both parents under 40 yielded the following data:
Number of children Number of families
—————————————–
More than 3 154
3 196
2 46
1 101
0 203
You wish to test the claim that the distribution of the number of children per family for families with both parents under 40 is the same as that of the U.S. as a whole. What is the value of the chi-square test statistic? (Note that expected frequencies are as follows: more than 3 children: 142.1; 3 children: 149.1; 2 children: 101.5; 1 child: 112.7; 0 children: 194.6.)
a. χ² = 32.091
b. χ² = 47.674
c. χ² = 13.781
d. χ² = 80.807
1. Different neighbourhoods may have different crime statistics. A sample of 10 days in Neighbourhood A revealed the following number of crimes per day:
15 12 16 17 15 14 16 10 12 14
A sample of 12 days in Neighbourhood B revealed the following number of crimes per day:
17 13 15 18 16 19 11 21 22 13 16 18
At a 5% level of significance, is there a difference in the crime rates for the two neighbourhoods?
2. Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 deliveries within a territory was selected. The delivery time and the number of cases delivered was recorded.
Customer Number of Cases Delivery Time (Minutes)
Customer Number of Cases Delivery Time (Minutes)
1 52 32.1 11 161 43.0
2 64 34.8 12 184 49.4
3 73 36.2 13 202 57.2
4 85 37.8 14 218 56.8
5 95 37.8 15 243 60.6
6 103 39.7 16 254 61.2
7 116 38.5 17 267 58.2
8 121 41.9 18 275 63.1
9 143 44.2 19 287 65.6
10 157 47.1 20 298 67.3
a) What is the coefficient of correlation for the variables “Number of Cases” and Delivery Time”? Is the correlation significant?
b) Derive a regression equation to predict delivery time based on the number of cases delivered.
c) Predict the delivery time for 150 cases of soft drink.
d) Is the regression significant at the 0.05 level?
e) What proportion of the variance in the delivery time is explained by the regression?
f) What is the standard error of the estimate?
g) Would it be appropriate to use the model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Why?
1. In a Gallup poll of 1,038 adults, 540 said that second-hand smoke is very harmful. What is the percentage of adults who said second-hand smoke is very harmful?
2. The first class in a relative frequency table is 50-59 and the corresponding relative frequency is 0.2. What does the 0.2 value indicate?
3. When you add the values 3, 5, 8, 12, and 20 and then divide by the number of values, the result is 9.6. Which term best describes this value: average, mean, median, mode, or standard deviation?
4. What is the range of the values 2.0, 3.7, 4.9, 5.0, 5.7, 6.7, 8.5, and 9.0?
What is the median?
What is the mean?
What is the mode?
Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana. Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A sample of 400 voters reveals that 300 would support her in the November election.
a. Estimate the value of the population proportion.
b. Compute the standard error of the proportion.
c. Develop a 99 percent confidence interval for the population proportion.
d. Interpret your findings.
Please see attachment and explain all work.
1) The distribution of actual weights of 8 oz. wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.1 ounces.
a) If a sample of five of these cheese wedges is selected, the probability that their average weight is less than 8 oz is?
a)__________________
b) There is only a 5% chance that the average weight of the sample of five of the cheese wedges will be below?
b)_________________
2) In an instant lottery, your chances of winning are 0.2. If you play the lottery five times and outcomes
are independent, the probability that you win at most once is?
2_________________
3) At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college are selected. Let X denote the number of Hispanics among them.
a) Find the mean of X a)__________________
b) Find the standard deviation of X b)_________________
Question:
The following stem and leaf display represents the final exam scores for a class of 25 literature students:
[Please refer to the attachment for the figure]
a. Convert the stem and leaf display into a frequency distribution, using a lower limit for the first class of 20 and a class width of 15. Complete the following frequency distribution table.
b. Using the frequency distribution table, calculate the mean exam score of the students.
c. Using the frequency distribution table, calculate the standard deviation of exam scores.
d. Construct a cumulative percentage of the given of examination scores
See the attached files.
Also, please see the formula sheet and standard normal distribution table to be used.
Only use a scientific or graphing calculator (Excel does not help me) and please show all working out.
Question 1
The following data set represents the oxygen uptake values for a random sample of 12 middle aged distance runners.
13 36 22 16 20 24 23 28 18 32 17 46
a. Calculate the mean oxygen uptake value.
b. Using the short-cut formula, calculate the standard deviation of oxygen uptake values.
c. Calculate the approximate value of the 40th percentile. What does this number tell you?
d. What is the percentile rank of the runner whose oxygen uptake was 32? What does this number tell you?
e. Calculate the median oxygen uptake.
f. Considering the relationship between the mean and median oxygen uptake, in what direction is this data skewed?
Question 2
An investor purchased 500 shares of Stock A at $10 per share, 300 shares of Stock B at $20 per share, and 100 shares of Stock C at $30 per share. What was the weighted mean price per share?
Please show all of the steps and processes used to solve each problem.
1. Suppose we are researching the attitudes of first year medical students at a local University. Using this example, describe in your own words how you would go about determining this through:
a. Drawing a random sample
b. Drawing a systematic sample
c. Drawing a convenience sample
2. Refer to the graphic ‘America’s students by grade level’. The latest Census report on schools found about 70 million students (27.8% of the population) from nursery school through college.
AMERICA’S STUDENTS BY GRADE LEVEL
Kindergarten/nursery school = 11.7%
Grades 1 – 8 = 44.9%
Grades 9 – 12 = 21.8%
College = 15.2%
Data from USA Today, 5/9/2000.
a. What is the population?
b. What information was obtained from each person?
c. Using the information given, estimate the number of students in college.
d. Using the information given, estimate the size of the entire U.S. population.
Please show all of the steps and processes you used to solve each of your problems.
Your company is developing a new radio communication system. Weight, power output, and frequency have each been identified by your engineering and productions staffs as being potential significant contributors to the production cost of a radio communication system. The following relationships between cost and these parameters have been hypothesized:
Cost will increase with increased radio weight.
Cost will increase with increased power output.
Cost will increase with increased frequency.
Your company collected first unit cost, weight, power output, and frequency data for fifteen radio communication systems that your company has previously manufactured. Your department head had a young summer intern who is familiar with performing linear regression using Microsoft Excel perform the following univariate and multivariate regressions using a 95% confidence interval.
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
The regression statistics developed by the intern are summarized in the accompanying Microsoft Excel spreadsheet entitled â??Radio Communication System Regression Statisticsâ?. However, the intern is not confident that he understands how to correctly interpret the regression statistics he has generated. Your department head is aware of your recently acquired expertise regarding interpreting linear regression statistics and has tasked you to analyze the regression statistics generated by the intern and answer the following:
11) Identify each of the following as either being a dependent variable, an independent variable, or not a variable.
a) Weight
b) Power
c) Cost
d) Frequency
e) System
12) Which of the following regression models fails to satisfy the common sense test criteria regarding the hypothesized correlation between the dependent variable and independent variable? (select all that apply)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) All of the above
e) None of the above
13) Which of the following regression models fails to satisfy the common sense test criteria regarding the statistical significance of the model as a whole? (select all that apply)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
14) Which of the following regression models fails to satisfy the common sense test criteria regarding the statistical significance of the strength of the relationship between the dependent variable and the independent variable(s)? (select all that apply)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
15) Which of the following models evidences the least probability of the observed R2 or Adjusted R2 values for the linear regression model being attributable to random chance as opposed to being attributable to an actual linear relationship existing between the dependent and independent variable(s)? (select one)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
16) Which of the following regression models explain less than 50% of the observed variation between the actual values of the dependent variable and the mean value of the dependent variable values for the sample data set? (select all that apply)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
h) None of the above
17) Which of the following regression models would result in the largest degree of error on average when using the model to predict the first unit cost for a new communication system? (select one)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
18) Which of the following regression models satisfy the requirement for the F-significance value associated with the model being less than or equal to the specified 0.05 statistical significance criterion? (select all that apply)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
h) All of the above
19) Which of the following regression models satisfy the requirement for the p-value associated with each independent variable associated with the model being less than or equal to the specified 0.05 statistical significance criterion? (select all that apply)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
20) Which of the following regression models evidences the strongest relationship between the dependent variable and the independent variable(s)? (select one)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
21) Which of the following regression models is the preferred regression model? (select one)
a) Cost vs. Weight
b) Cost vs. Power
c) Cost vs. Frequency
d) Cost vs. Weight and Power
e) Cost vs. Weight and Frequency
f) Cost vs. Power and Frequency
g) Cost vs. Weight, Power and Frequency
3. A sample of 49 households is taken from a population in which the standard deviation is 7. The standard error of the mean isPlease see the attached file.
4. It is desired to construct a 95% confidence interval. The correct value of Z to obtain for the 95% confidence interval is: …
5. A confidence interval has been constructed with total width of 50 units. If the sample mean is 100, the lower bound of the interval is …
6. Hogan Company has constructed a new assembly line for mixing paint of various colors and consistencies. A recent sample of 200 one-gallon cans yielded that 2 were improperly mixed. What sample size is required in order to construct a 95% confidence interval (z = 1.96) in the next study and get to within +/- 0.5% of the true percentage of defective cans of paint being assembled?
7. The management of Fast Airlines tracks the proportion of the company’s passengers that are flying on business trips. An on-board preliminary study conducted last year revealed that 34% of the passengers were involved in a business venture. What sample size is required in order to construct a 95% confidence interval (z = 1.96) in the next study and get to within +/- 1% of the true percentage of business flyers? …
[See the attached questions file.]
1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.
A special insulation will lower your heating bills by less than $78.
2. (TCO 11) A 15-minute Oil and Lube service claims that their average service time is no more than 15 minutes. A random sample of 35 service times was collected, and the sample mean was found to be 16.2 minutes, with a sample standard deviation of 3.5 minutes. Is there evidence to support, or to reject the claim at the alpha = 0.05 level? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.
Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic,
Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is
the correctness of the prediction different for the two types of cola drinkers? Could you identify
your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample
z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which
test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.)
3.3 You are the member of the marketing team at Sara Bellum’s Pizza – the pizza for people who think too much!! Your mission is to evaluate two locations and determine if there is any difference in their suitability as locations for the next Sara Bellum Pizza restaurant. You will use a level of significance of 0.05.
The locations are in the same neighborhood. There is site A and site B. It has been determined that a best measure of the success of a Sara Bellum Pizza restaurant is based on the pizza purchasing tendencies of those folks in a 1 mile radius of the store. Specifically – if they buy pizza at least once in the past two weeks they are considered a frequent purchaser. Residents in a one mile radius of each prospective location were asked about their pizza purchase tendencies. Residents around site A indicated that 240 of them had bought pizza in the past two weeks- and 260 of them did not. Around site B — 255 residents indicated that they had bought pizza in the past two weeks and 245 of them indicated that they did not.
(A) Present the contingency table for this information about sites A and B and good preference and poor preference.
(B) What is the null hypothesis for the problem you have been asked to solve?
What is the alternate hypothesis?
What is the critical value for the chi-squared distribution??
What is the decision rule??
(C) Calculate the chi-squared value.
Show the work of the calculations.
Decide. Inform.
The owner of a restaurant serving Continental-style entrees has the business objective of learning more about patterns of patron demand for the Friday to Sunday weekend time period. Data were collected on 630 customers on the type of course ordered and are listed in the table below.
Type of Entry Number Served
Beef 187
Chicken 103
Mixed 30
Duck 25
Fish 122
Pasta 63
Shellfish 74
Veal 26
a. Construct a percentage summary table for he types of entree’s ordered.
b. Construct a bar, pie and Pareto diagram for the entrees ordered.
b. Do you prefer a Pareto diagram or a pie chart for these data? Why?
c. What conclusions can the restaurant owner draw concerning demand for different types of entrees?
Please see the attached file.
Identify the type of chart or graph and what this type of chart or graph is usually used to depict. Was the proper graph or chart used to represent this data? Why or why not? Was this the best way to display the data? What other types of graphs could have been used? Is the scope and scale of the graph appropriate? Why or why not? Does the graph support the findings in the article? Why or why not?
Talk Time on a Cell Phone: Suppose the ‘talk time’ in digital mode on a Motorola Timeport P8160 is
normally distributed with mean 324 minutes and standard deviation 24 minutes.
(a) What percent of the time will a fully charged battery last at least 330 minutes?
(b) What is the probability that a random sample of n = 15 batteries results in a mean talk time
of at least 330 minutes?
(c) What is the probability that a random sample of n = 30 batteries results in a mean talk time
of at least 330 minutes?
1. Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 9 population means (from equal sized samples) are not all equal. What should we expect?
2. Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 6 population means are not all equal. What should we expect?
1. Do you think that it is possible to make a decision with one-hundred percent certainty? What are possible elements you may consider before making a business decision so that you can minimize uncertainty in your decision?
2. What are possible elements you may consider as a manager before making a business decision so that you can minimize uncertainty in your decision.
Please see attached
Chapter 10, exercise number 18
18. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?
A. Analysis of variance (ANOVA) is used to determine if there is a difference between the means of different populations. For example, I had a student in Prescott who raised hens. A company was trying to sell her the feed they produced by claiming that if her hens ate their feed the hens would produce more eggs. They offered her a study to read in which they demonstrated that their feed was the best. To support this they conducted an experiment in which they fed four different types of food, including their own, to groups of hens. They wanted to show that on average hens that ate their food produced more eggs. They used analysis of variance. This is a true story. Can you think of examples at work in which ANOVA is used or could be used?
B. The personnel manager of a large finance company wished to evaluate the effectiveness of 4 different sales-training programs designed for new employees. A group of 32 recently hired employees are randomly assigned to the 4 training programs so that there are 8 subjects in each program. At the end of the program an exam is given and the scores are as follows;
PROGRAM
A B C D
66 72 61 63
74 51 60 61
82 59 57 76
75 62 60 84
73 74 81 58
97 64 55 65
87 78 70 69
78 63 71 80
C. At a five percent significance level, use the one-way ANOVA to determine if there is evidence of a significant difference in the fore training programs?
D. Suggest applications of nonparametric methods to solving business related problems. Describe the example. How are you or could you use nonparametric methods to solve business related problems?
E. Surveys are used to facilitate marketing efforts by assessing both potential customers’ evaluations of products and the characteristics of the same customers. In other words, surveys provide the data necessary to use the chi-square distribution to test hypotheses related to whether or not a statistically significant relationship exists between the characteristics of customers and their evaluation of products. With this in mind, propose survey questions to evaluate customers’ preferences for a good or service you are familiar with and also questions designed to identify the characteristics of these customers.
Show all work for Problems 2 and 18; Check answers for 6 only.
2. The student population at the state college consists of 55% females and 45 % males.
a. The college theater department recently staged a production of a modern musical. A researcher recorded the gender of each student entering the theater and found a total of 385 females and 215 males. Is the gender distribution for theater goers significantly different from the distribution for the general college? Test at the /05 level of significance.
b. The same researcher also recorded the gender of each student watching a men’s basketball game in the college gym and found a total of 83 females and 97 males. Is the gender distribution for basketball fans significantly different from the distribution for the general college? Test at the .0555 level of significance.
6. Langewitz, Izakovic, and Wyler (2005) reported that self-hypnosis can significantly reduce hay fever symptoms. Patients with moderate to severe allergic reactions were trained to focus their minds on specific locations where their allergies do not bother them, such as a beach or a ski resort. In a sample of 64 patients who received this training, suppose that 47 showed reduced allergic reactions and 17 showed an increase in allergic reactions. Are these results sufficient to conclude that the self-hypnosis has a significant effect? Assume that increasing and decreasing allergic reactions are equally likely if the training has no effect. Use a-.05
H0: The training has no effect and that increasing and decreasing are equally likely, Fe=pm=1/2(64)=32
H1: The training does have a significant effect
Assumptions: Expected frequencies â?¥5
a=.05
df=1
Critical regio=3.84
Test value x^(2=â?'(Fo-Fe)^2 )=(47-32)²+(17-32)²
Fe 32 32
=14.06
X²=14.06 falls in reject H0 region
Conclude that the training has a significant effect on allergic reactions
18. Reseaech results suggest that IQ scores for boys are more variable than IQ scores for girls(Arden & Plomin, 2006). A typical study looking at 10-year old children classifies participants by gender and by low, average, or high IQ. Following are hypothetical data representing the research results. Do the data indicate a significant difference between the frequency distribution for males and females? Test at the .05 level of significance and describe the difference.
Low IQ Avg High
Boys 18 42 20 80
Girls 12 54 14 80
n=160
See attached file.
Please provide detailed explanations and show all work.
16. The employee benefits manager of a small private university would like to estimate the proportion of full time employees who like to adopt the first (i.e. plan A) of three available health care plans in the coming enrolment period. A reliable frame of the universities employees and their tentative healthcare preferences are given on the spreadsheet labeled (Question 16/18)
a. Use excel to choose a simple random sample of size 45 from the given frame
b. Using the sample found in part A, construct a 99% confidence interval for the proportion university employees who prefer plan A. Assume that the population consists of the preferences of all employees in the given frame.
c. Interpret the 99% confidence interval constructed in part B.
18. Continuing problem 16, select simple random samples of 30 individuals from each given employee classifications (i.e. administrative staff and faculty). Construct a 99% confidence interval for the proportion of employees who prefer adopting plan A for each of the three classifications. Do you see evidence of significant differences among these three interval estimates? Summarize your findings
26. Consider a random sample from 100 households is a middle class neighborhood that was the recent focus of an economic development study conducted by the local govt. Specifically, for each of the 100 households, information was gathered on each of the following variables: family size, location of whether those surveyed owned or rented their home, gross annual income of this first household wage earner ( if applicable) , monthly home mortgage or rent, average expenditures on utilities, and the total indebtedness (excluding the value of a home mortgage) of the household. That data is provided on spread sheet titled (prob 26)
a. Separate the households in the sample by location of their residence within the given community. For each of the 4 locations, use the sample information to generate a 90% confidence interval for the mean annual income of all relevant first household wage earners. Compare these 4 interval estimates. You may also want to consider generating box plots of the primary wage earner variable for households in each of the 4 given locations.
b. Generate a 90% confidence interval for the difference between the mean annual income levels of the first household wage earners in the first (i.e. SW) and second (i.e. NW) sectors of the community. Generate similar 90% confidence intervals for the differences between the mean annual income levels of primary wage earners from all other pairs of locations (i.e. first & third, first & fourth, second and third, second and fourth, and third and fourth) summarize your findings
6. A study is performed in a large southern town to determine whether the average weekly grocery bill per four person family in the town is significantly different from the national average. A random sample of the weekly grocery bills of four person families in this town can be found on spreadsheet labeled (problem 6)
a. Assume that the national average weekly grocery bill for a four person family is $100. Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?
b. For which values if the sample mean (i.e. average weekly grocery bill) would you decide to reject the null hypothesis at alpha =0.01 significance level? For which values of the sample mean would you decide to reject the null hypothesis at the alpha =0.10 level?
44. A finance professor has just given a midterm exam in her corporate finance course. In particular she is interested in determining whether the distribution of 100 exam scores is normally distributed. The data is spreadsheet labeled (problem 44). Perform a chi-square goodness of fit test. Report and interpret the computed p value. What can you conclude about normality?
See attached data file.
In each of the assignments in this course, you will be dealing with the following scenario: American Intellectual Union (AIU) has assembled a team of researchers in the United States and around the world to study job satisfaction. Congratulations, you have been selected to participate in this massive global undertaking.
The study will require that you examine data, analyze the results, and share the results with groups of other researchers. Job satisfaction is important to companies large and small, and understanding it provides managers with insights into human behavior that can be used to strengthen the company’s bottom line.
The data set for the study is a sample of a survey conducted on the population of the American Intellectual Union (AIU). It is available via the following link: Excel 2007 DataSet with DataSet Key which contains the following nine sections of data that will be used throughout our course:
â-¦Gender
â-¦Age
â-¦Department
â-¦Position
â-¦Tenure
â-¦Overall Job Satisfaction
â-¦Intrinsic Job Satisfaction – Satisfaction with the actual performance of the job
â-¦Extrinsic Job Satisfaction – external to the job, for example, office location, your work colleagues, your own office (cubicle/hard walled office, etc),
â-¦Benefits – Health insurance, pension plan, vacation, sick days, etc.
In the first assignment you are to complete the following:
– You will need to examine two of the nine sections of data:
one section of qualitative data (choose either Gender or Position)
one section of quantitative data (choose either Intrinsic or Extrinsic)
– Each section should include all data points listed in the column for the variable. The requirements include:
1. Identify the data you selected.
2. Explain why the data was selected.
3. Explain what was learned by examining these sets of data.
4. Your analysis should include using Microsoft Excel to obtain information about the data through the use of three measures of central tendency (mean, median, mode).
5. Your analysis should also include the use of two measures of variability (standard deviation and variance). Some measures are appropriate for qualitative data, and some are appropriate for quantitative data.
6. If a measure is not applicable, then explain why.
7. You will have to also provide one chart/graph for each of the results of the two processed sections of data (2 total), such as a pie or bar chart or a histogram. (A table is not a chart/graph.) Ensure that you label the chart/graph clearly.
8. You will then need to discuss what you additionally learned from the results of this process.
9. Explain why charts/graphs are important in conveying information in a visual format and why standard deviation and variation are important.
You will need to combine all of the items above into one comprehensive report. This report must be completed in Microsoft Word and should contain: Gender Age Department Position Tenure Job Satisfaction Intrinsic Extrinsic Benefits
1 1 3 2 3 5.2 5.5 6.8 1.4
1 1 1 1 3 5.1 5.5 5.5 5.4 KEY TO SURVEY
1 1 1 1 1 5.8 5.2 4.6 6.2
1 1 2 1 1 5.5 5.3 5.7 2.3 Demographics
1 1 2 1 1 3.2 4.7 5.6 4.5
2 2 2 1 1 5.2 5.5 5.5 5.4 Gender
2 2 1 1 1 5.1 5.2 4.6 6.2 1 Male
2 2 1 1 1 5.8 5.3 5.7 2.3 2 Female
2 2 2 1 2 5.3 4.7 5.6 4.5 Age
2 2 2 1 2 5.9 5.4 5.6 5.4 1 16 – 21
1 2 2 2 2 3.7 6.2 5.5 6.2 2 22 – 49
2 2 1 1 1 5.1 5.2 4.6 6.2 3 50 – 65
2 2 1 1 1 5.8 5.3 5.7 2.3 Department
2 2 2 1 2 5.3 4.7 5.6 4.5 1 Human Resources
2 2 2 1 2 5.9 5.4 5.6 5.4 2 Information Technology
1 2 2 2 2 3.7 6.2 5.5 6.2 3 Administration
1 2 2 2 2 5.5 5.2 4.6 6.2 Position
2 2 1 1 1 5.8 5.3 5.7 5.4 1 Hourly Employee (Overtime Eligible)
2 2 2 1 2 5.3 4.7 5.6 6.2 2 Salaried Employee (No Overtime)
1 1 2 1 1 5.5 5.3 5.7 2.3 Tenure With Company
1 1 2 1 1 3.2 4.7 5.6 4.5 1 Less than 2 years
2 2 2 1 1 5.2 5.5 5.5 5.4 2 2 to 5 years
2 2 1 1 1 5.1 5.2 4.6 6.2 3 Over 5 Years
2 2 1 1 1 5.8 5.3 5.7 2.3
1 2 2 2 2 3.7 6.2 5.5 6.2 Four Survey Measures
2 2 1 1 1 5.1 5.2 4.6 6.2
2 2 1 1 1 5.8 5.3 5.7 2.3 SURVEY MEASURE #1 OVERALL JOB SATISFACTION (Scale 1-7)
2 2 2 1 2 5.3 4.7 5.6 4.5 1 = Least Satisfied
2 2 2 1 2 5.9 5.4 5.6 5.4 7 = Most Satisfied
1 2 2 2 2 3.7 6.2 5.5 6.2 SURVEY MEASURE #2 INTRINSIC JOB SATISFACTION (Scale 1-7)
1 2 2 2 2 5.5 5.2 4.6 6.2 1= Least Satisfied
2 2 1 1 1 5.8 5.3 5.7 5.4 7= Most Satisfied
2 2 1 1 1 5.8 5.3 5.7 2.3 SURVEY MEASURE #3 EXTRINSIC JOB SATISFACTION (Scale 1-7)
2 2 2 1 2 5.3 4.7 5.6 4.5 1 = Least Satisfied
2 2 2 1 2 5.9 5.4 5.6 5.4 7 = Most Satisfied
1 2 2 2 2 3.7 6.2 5.5 6.2 SURVEY MEASURE #4 BENEFITS (Scale 1-7)
1 2 2 2 2 5.5 5.2 4.6 6.2 1= Least Satisfied
1 2 2 2 2 5.5 5.2 4.6 6.2 7= Most Satisfied
1. An experimenter is studying the effects of temperature, pressure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.
a. If any particular experimental run involves the use of a single temperature, pressure, and catalyst, how many experimental runs are possible?
b. How many experimental runs are there that involve use of the lowest temperature and two lowest pressures
2. The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables.
a. T = the total number of pumps in use
b. X = the difference between the numbers in use at stations 1 and 2
c. U = the maximum number of pumps in use at either station
d. Z = the number of stations having exactly two pumps in use
The dataset contains a sub-sample of 308, 4th and 6th grade students from Michigan created by Chase and Dummer. In this dataset we posit the question, “Are students personal goals choices related to their gender, and does this relationship differ by grade level?”
In the answer, you will investigate the relationship between student’s goals and gender by their grade level.
a) Are student’s choices for personal goals related to their gender? What is the nature of the relationship? (cite table/figure ) (cite the proper table and/or graph)
b) When students are divided into in grade level “slices,” (fourth and sixth grades) what is the nature of the relationship between student’s goals and their gender, and how does the relationship compare across grade level slices? (cite the proper table and/or graph)
How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise…
a) We are willing to regard the wood pieces prepared for the lab session as an SRS of all similar pieces of Douglas fir. Engineers also commonly assume that characteristics of materials vary Normally. Make a graph to show the shape of the distribution for these data. Does the Normality condition appear safe? Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation 3000 pounds.
b) Give a 90% confidence interval for the mean load required to pull wood apart.
The above exercise gives data on the pounds of load needed to pull apart pieces of Douglas fir. The data are a random sample from a Normal distribution with standard deviation 3000 pounds.
a) Is there significant evidence at the α = 0.10 level against the hypothesis that the mean is 32,000 pounds for the two-sided alternative?
b) Is there significant evidence at the α = 0.10 level against the hypothesis that the mean is 31,500 pounds for the two-sided alternative?
(Please see attachment and show all work).
Please read the questions carefully and use Excel to solve the problems. Thank you.
One hundred people were asked which of four brands of Cola they preferred…
(The material covers Chi-Square Goodness of Fit Tests, Contingency Tables, One-Factor Analysis of Variance, and Two-Factor Analysis.)
(Please use Excel to solve these questions and explain your solution and provide evidence of your work.)
Part 1 1. Use the ANOVA table SV—-SS—–DF—-MS—-F Between 64—————8 Within————-2—— Total 100—————– SSB = 64, SST = 100, MSW = 2, F = 8
a. The number of degrees of freedom corresponding to between treatments is?
b. The number of degrees of freedom corresponding to within treatments is?
c. The mean square between treatments (MSB) is?
Please note: right here we are using different terminology:
1. Sum of squares due to treatments (SSTR) is equivalent to Sum of Squares Between (SSB)
2. Mean Square due to treatment (MSTR) is equivalent to Mean Square Between (MSB)
3. Sum of Squares due to error (SSE) is equivalent to Sum of Squares Within (SSW)
4. Mean Square due to error (MSE) is equivalent to Mean Square Within (MSW)
Therefore F= MSTR/MSE = MSB/MSW and SST = SSTR + SSE = SSB+SSW **************************
Part 2 1. In a random sample of 50 women, 32 reported that they favor the Redskins to win the Superbowl, while in a sample of 100 men, 70 favored the Redskins to win.
a. the point estimate of the difference between the proportions of the two populations is?
b. the standard error of the difference between the proportions of the two populations is?
c. the 95% confidence interval for the difference between the proportions of the two populations is?
2. A sample of 1000 adults and teens found the following; Coffee drinkers: 100 teens, 300 adults, total 400 Tea drinkers: 50 teens, 100 adults, total 150 Soda drinkers: 200 teens, 200 adults, total 400 Other beverages: 25 teens, 25 adults, total 50 Total teens: 375 Total adults: 625 We are testing for independence between age (adult and teen)
a. with a .05 level of significance, the critical value for the test is?
b. the expected number of adults who prefer soda is?
c. the calculated value for the test for independence is?
PLEASE explain and show all calculations.
I need some help with this…please show how you arrived at solution.
The number of touchdowns scored in each game during one season by a team contending for a national championship was: 2 8 2 5 0 6 6 3 6 4 2 Consider this data as the entire population of all eleven games played. a. Find the mean, median, and mode number of touchdowns per game. b. Find the range, variance, and standard deviations
1. Generate a normal distribution graph of all the combined data using Microsoft Excel.
Please refer to spreadsheet attach below:
Typical Seasonal Demand for Summer Highs
Actual Demands (in units)
Month Year 1 Year 2 Year 3 Year 4
1 18,000 45,100 59,800 35,500
2 19,800 46,530 30,740 51,250
3 15,700 22,100 47,800 34,400
4 53,600 41,350 73,890 68,000
5 83,200 46,000 60,200 68,100
6 72,900 41,800 55,200 61,100
7 55,200 39,800 32,180 62,300
8 57,350 64,100 38,600 66,500
9 15,400 47,600 25,020 31,400
10 27,700 43,050 51,300 36,500
11 21,400 39,300 31,790 16,800
12 17,100 10,300 31,100 18,900
Avg.
The Bookstall, Inc., is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are $1.00 each, and hardcover books are $3.50. Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?
The t distribution is a continuous distribution (Points : 6)
True
False
2. A confidence interval for a population mean (Points : 6)
estimates the population range
estimates a likely interval for a population mean
estimates a likelihood or probability
estimates the population standard deviation
3. A 95% confidence interval infers that the population mean (Points : 6)
is between 0 and 100%
is within ± 1.96 standard deviations of the sample mean
is within ± 1.96 standard errors of the sample mean
is too large
4. What is the interval within which a population parameter is expected to lie? (Points : 6)
Sample
Expected Value
Standard Deviation
Confidence Interval
5. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):
One-Tailed
Two-Tailed
95% (or .05) significance level Question 5.
99% (or .01) significance level
(Points : 6)
-2.58 and 2.58
-1.65 or 1.65
-1.96 and 1.96
-2.33 or 2.33
6. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):
One-Tailed
Two-Tailed
95% (or .05) significance level
Question 6.
99% (or .01) significance level
(Points : 6)
-2.58 and 2.58
-1.65 or 1.65
-1.96 and 1.96
-2.33 or 2.33
7. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):
One-Tailed
Two-Tailed
95% (or .05) significance level
99% (or .01) significance level
Question 7.
(Points : 6)
-2.58 and 2.58
-1.65 or 1.65
-1.96 and 1.96
-2.33 or 2.33
8. Please choose the appropriate answer for the cut-off/critical value ranges to go in the blank for each question (5-8):
One-Tailed
Two-Tailed
95% (or .05) significance level
99% (or .01) significance level
Question 8.
(Points : 6)
-2.58 and 2.58
-1.65 or 1.65
-1.96 and 1.96
-2.33 or 2.33
9. To determine the size of a sample, the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population. (Points : 6)
True
False
10. The t distribution is based on the assumption that the population of interest is normal or nearly normal. (Points : 6)
True
False
11. Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500
What is the best point estimate of the population mean?
(Points : 6)
$25,000
$2,500
$400
$62.50
12. Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500.
What is the 95% confidence interval for the mean salary of all graduates from the English Department?
(Points : 6)
[$22,500, $27,500]
[$24,755, $25,245]
[$24,988, $25,012]
[$24,600, $25,600]
13. Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000 with a standard deviation of $2,500.
What do the confidence interval results mean?
(Points : 6)
The population mean is in the interval
The population mean is not in the interval
The likelihood that any confidence interval based on a sample of 400 graduates will contain the population mean is 0.95
There is a 5% chance that the computed interval does not contain the population mean.
14. The proportion of junior executives leaving large manufacturing companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of junior executives leaving within three years was 21. To update this study, the files of how many junior executives should be studied?
(Points : 6)
594
612
709
897
15.
7. There are 2,000 eligible voters in a precinct. 500 of the voters are selected at random and asked to indicate whether they planned to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they were going to vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?
(Points : 6)
0.647 and 0.753
0.612 and 0.712
0.397 and 0.797
0.826 and 0.926
16. In opening a new Curves, the company advertises that, while on the Curves diet and workout routine, new members lose an average of 10 pounds in the first two weeks with a population standard deviation of 2.8 pounds. A random sample of 50 women who joined the program revealed a mean loss of 9 pounds. At a .05 level of significance, use the steps in hypothesis testing to see if we can conclude that those joining Curves on average will lose less than 10 pounds.
Is this a one-tailed or two-tailed test?
(Points : 5)
One Tailed
Two Tailed
17. In opening a new Curves, the company advertises that, while on the Curves diet and workout routine, new members lose an average of 10 pounds in the first two weeks with a population standard deviation of 2.8 pounds. A random sample of 50 women who joined the program revealed a mean loss of 9 pounds. At a .05 level of significance, use the steps in hypothesis testing to see if we can conclude that those joining Curves on average will lose less than 10 pounds.
What is the cut-off (critical) value?
(Points : 5)
+/- 1.65
+/- 1.96
+/- 2.33
+/- 2.58
What is the purpose of developing a frequency distribution?
What is the relationship between the relative frequency and the cumulative frequency?
1. Find the mean of the distribution shown.
x 1 2
P(x) 0.31 0.69
A) 0.96
B) 1.42
C) 1.18
D) 1.69
2. For a normal distribution with mean 5 and standard deviation 6, the value 11 has a z value of
A) -1
B) 1
C) 2
D) 3
3. If the standard deviation of a probability distribution is 6.25, the variance is 2.30
True/False
4. A stem and leaf plot is useful for keeping more precision than a grouped frequency distribution.
True/False
5. What kind of relationship does the scatter plot show between x and y?
A) A positive linear relationship C) No linear relationship
B) A negative linear relationship D) This is not a scatter plot
[Please efer to the attachment for the scatter-plot].
6. A researcher conducted a study to record the colors of students’ eyes. The appropriate measure(s) of central tendency is (are):
A) The mode
B) The median
C) The mean
D) Both the mode and the median
If 70 percent or more of the old bricks in a brickyard meet certain standards, it will be profitable to hire persons to sort the bricks. According to past experience with this brickyard, on average 70% of all the old bricks meet these standards. A random sample of 100 old bricks is taken from all the (many, many) bricks in the brickyard and the bricks are examined to see if they meet the standards.
Let X = the number of bricks in the sample that meet the standards
Let (p-hat = the sample proportion of bricks meeting the standards
a) Explain how the sample proportion (p-hat) is distributed in this sample
(p-hat is a _____ RV with ______because….)
b) Find the probability that the sample proportion, p-hat is between 0.61 and 0.79.
c) If 60% of bricks are found to conform to the standards, is it likely that the true proportion of old bricks meeting the standards is at least 70%? Explain briefly.
In contract negotiations, a company claims that a new incentive scheme has resulted in average weekly earnings of at least $400 for all customer services workers. The union is skeptical. A union representative, recalling his college statistics course, decides to test the company’s claim. She takes a random sample of 81 workers and finds that these workers have average weekly earnings of $385 with a sample standard deviation of $45. The representative uses H0: μ = $400 and HA < $400 and a significance level of 0.025.
a) Why didn’t the union representative choose μ ≠ $400?
b) What is the appropriate estimator for this test? Explain exactly how the estimator is distributed for this hypothesis test. (____is a ____ RV with ____ because)
c) Write out the decision rule for this test.
d) Using a significance level of 0.025, should the null hypothesis be rejected?
e) Is the company’s claim correct?
A supervisor for a large company wishes to estimate the proportion of parts from a supplier that are defective. He has selected a random sample of n = 200 incoming parts and has found 11 to be defective. Based on a 95% confidence level, the upper and lower limits for the confidence interval estimate are approximately 0.0234 to 0.0866
True or False?
Which of the tools for decision making (quantitative methods, qualitative methods, and triangulation methods) should be used in developing operating procedures? Justify and explain your response.
See attachment for problem
A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location.
Research question: At α = .05, does vehicle type vary by mall location?
Pax World Balanced: x with line over it= 9.58%;s= 14.05%
Vanguard Balanced Index : x with line over it = 9.02%;s = 12.50%
These are the means and standard deviations of annualized percent returns.
A) compute the coefficient of variation for each fund. If x (with line over it)represents return and s represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return.From this point of view, which fund appears to be better? Explain.
B) compute a 75% Chebyshev interval around the mean for each fund. Use the intervals to compare the two funds. As usual, past performance does not guarantees future performance.
Did you ever purchase a bag of M&M Peanut candies and wonder about the distribution of the colors? A recent article reported that 30 percent of the candies are brown, 20 percent yellow, 20 percent red, 20 percent green, and 10 percent orange. A one-pound bag of M&M peanut candies was purchased at Wal-Mart here in Lubbock. A total of 188 candies were in the bag, with 67 brown, 22 yellow, 51 red, 24 green, and 24 orange.
Using the chi-square goodness-of-fit test and the .05 level of significance, determine whether or not this agrees with the expected distribution (show all steps). Write a brief explanation of your conclusion.
29. A test measuring the knowledge of the U.S. Constitution has been given to a national sample of 6000 high school seniors. The distribution of scores approximates the normal curve and has a mean of 79 and a standard deviation of 6.5.
a. what percentage of those tested scored 68 or below?
b. how many of the 6000 individuals scored between 68 and 87?
c. I want to give the top 7% of the students a prize for doing
such a great job on the exam. What would be the lowest score
eligible for a prize?
The following lists two variables taken from a survey of recent college graduates:
Cumulative First year’s salary
College GPA (in 1,000’s
Joe 3.1 28
Suzy 2.5 22
Catherine 3.6 29
Simon 2.8 25
Jethro 2.7 27
Shannon 3.3 30
Vonda 3.4 32
Zane 3.5 28
Use the data to answer the following:
a. Draw a scatter diagram depicting the relationship between these two variables. Interpret.
b. Calculate the coefficient of correlation. Interpret.
c. Calculate the coefficient of determination. Interpret.
d. Use our 5-step hypothesis test procedure to determine whether or not the correlation you calculated in part “b”
is significant. Interpret.
e. Disregarding your finding in part “d,” develop a regression equation for this data.
f. Using your regression equation, what would you predict Geraldine’s first year salary to be if she graduated with a 3.15 G.P.A.?
g. What is the standard error of estimate? Interpret.
Independent simple random samples from two groups of patients used in an clinical trial yielded the following measurements on glucose levels following a new drug treatment:
Group A: 54, 99, 105, 46, 70, 87, 55, 58, 139, 91, 102, 110
Group B: 93, 91, 93, 150, 80, 104, 128, 83, 88, 95,94, 97
Do these data provide sufficient evidence to indicate that the mean of group A is different than the mean of Group B? Let alpha=0.05.
What’s null hypothesis for this research question?
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22. Q22
What assumptions do we test before running the statistical test? SHOW your results on the test. Just write down the key numbers (including tests, statistics, p value and your conclusions) without copying and pasting SPSS output tables.
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23. Q23
What test do you plan to conduct to test the hypothesis? WHY? What’s your conclusion on hypothesis testing? Show the key evidence (statistic, p value, conclusion on hypothesis testing) to support your conclusions without copying and pasting SPSS output tables. (max 100 characters)
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A team of introductory statistics students (with too much free time) when to Marsh and recorded the calories and fat for various kinds of soup. Write a succinct summary of the central tendency, dispersion, and shape of the data.
[See the attached Data File.]
Problem 1
Consider the following prices and accuracy ratings for 27 stereo speakers.
(a) Make a scatter plot of accuracy rating as a function of price.
(b) Calculate the correlation coefficient. At ? = .05, does the correlation differ from zero?
(c) In your own words, describe the scatter plot. (Data are from Consumer Reports 68, no. 11 [November 2003], p. 31.
(d) Develop the regression equation. Interpret the slope and the Y-intercept
[Please refer to the attachment for the data]
Problem 2
A study is conducted concerning automobile speeds and fuel consumption rates. The following data is collected:
Speed MPG
44 22
51 26
48 21
60 28
66 33
61 32
a. Plot these data in a scatter diagram.
b. Compute the coefficient of correlation. Explain
c. Compute the coefficient of determination. Explain.
d. Determine the regression equation. Interpret the regression equation. Where does the equation cross the Y-axis?
Problem 3
Tem Rousos, president of Rousos Ford, believes there is a relationship between the number of new cars sold and the number of sales people on duty. To investigate he selects a sample of eight weeks and determines the number of new cars sold and the number of sales people on duty for that week.
Week Sales staff Cars sold
1 5 53
2 5 47
3 7 48
4 4 50
5 10 58
6 12 62
7 3 45
8 11 60
a. Plot these data in a scatter diagram.
b. Compute the coefficient of correlation. Explain
c. Compute the coefficient of determination. Explain
d. Determine the regression equation. Interpret the regression equation. Where does the equation cross the Y-axis? How many additional cars can the dealer expect to sell for each additional salesperson employed?
Problem 4
Listed below is the net sales in $ million for Home Depot, Inc., and its subsidiaries from 1993 to 2004.
YEAR NET SALES
1993 9,240
1994 12,355
1995 15,456
1996 19,873
1997 24,913
1998 30,125
1999 38,423
2000 45,989
2001 53,564
2002 58,654
2003 64,290
2004 73,675
Determine the least squares equation. On the basis of this information, what are the estimated sales for 2005 and 2006?
Counting without Counting ???
Let me tell you a little dirty secret about the mutual dislike between mathematicians and physicists. It can escalate into a full blown war if diplomacy is not attempted properly.
It happens that a graduate student in theoretical/mathematical physics is looking for five members for his dissertation committee. He has been working closely with three professors in the mathematics department, and 5 professors in the physics department on his dissertation research.
Now comes the monkey wrench.
The mathematics department demands that the chair of the dissertation committee must be a mathematician in order to keep the physicists in check. What? How arrogant! But, there is no other choice if a dissertation committee has to be assembled in time.
Please figure out how may ways this graduate student can choose among his beloved professors, if the chair of the committee must be a mathematician, and the rest of the committee can be a mix of mathematicians and physicists. Post your collaborative group response by Sunday September 26th at midnight Eastern Time.
1) If the correlation coefficient r is equal to 0.57, find the coefficient of determination.
a) 0.68
b) 0.75
c) 0.45
d) 0.32
2) The prediction interval around y’ for a specific x is
a) A confidence interval for the true mean value of the y values that correspond to that x
b) The value of y used to calculate the slope of the regression line
c) The interval of values of x used to predict y’
d) The difference between the value of y and the value of x
3) What is the critical t-value for a right-tailed test when a=0.025 and d.f. = 12?
a) 2.179
b) 2.831
c) 2.228
d) 1.869
4) A portion of an ANOVA summary table is shown below.
Source sum of squares degrees of freedom
Between 22 2
Within(error) 39 34
Total 61
a) dfN = 2, dfD = 34
b) dfN = 34, dfD = 2
c) dfN = 22, dfD = 39
d) dfN = 39, dfD = 22
5) If r = -0.726 and n = 6, test the significance of the correlation coefficient at a = .05
a) Reject p=0 because 2.91 > 2.57
b) Do not reject p=0 because -2.11 < 2.57
c) Do not reject p=0 because -2.11 < 2.54
d) Do not reject p=0 because 2.91 < 2.54
6) Use a P- value to test the claim about the population mean, m # 230; using the given sample statistics. State your decision for alpha = 0.05
Claim: m # 230; Sample statistics: x (bar) = 216.5, s = 17.3, n = 48
7) Use a t-test to investigate the claim and assume that the population is normally distributed:
A large university says the mean number of classroom hours per week for full-time faculty is more than 9. A random sample of the number of classroom hours for full-time faculty for one week is listed. At alpha = 0.05, test the university’s claim.
10.7 9.8 11.6 9.7 7.6 11.3 14.1 8.1 11.5 8.5 6.9
Please explain all work.
In order for a lifestyle change to be considered effective, the target is to have the average cholesterol of this group be below 200. After 6 months of exercising more and eating better, an SRS of 51 patients at risk for heart disease had an average cholesterol of x = 192, with a standard deviation s = 21. Is this sufficient evidence that eating better and exercising more is effective in meeting the target? Assume the distribution of the cholesterol for patients in this group is approximately Normal with mean μ.
a) State the null and Alternative hypotheses H0:
Ha:
b) What are the degrees of freedom?
c) Find the one-sample t-statistic
d) Use the t-table to estimate the P-value and state your conclusion in words of this problem
e) Find a 95% confidence interval for the average cholesterol of patients at risk for heart disease who have been on the diet for 6 months
Problem 1: Consider three identical items in parallel. What is the system reliability if each item has a reliability of 98%?
Please explain why the exponential function is used for reliability.
What is the difference between an independent and a dependent variable?
Does a regression model imply causation? Why or why not?
Provide an example which provides and independent and dependent variable from your place of work.
A description of how you believe statistics can enrich and represent the results of a study, and an explanation of how statistics can be used to misrepresent the results of a study.
Please show detailed solutions.
Does cocaine use by pregnant women cause their babies to have low birth weight?
To study this question, birth weights of babies of women who tested positive for cocaine/crack during a drug-screening test were compared with the birth weights for babies whose mothers either tested negative or were not tested, a group we call “other”
Here are the summary statistics. The birth weight s are measured in grams.
Group n Sample mean Standard deviation s
Positive test 134 2733 599
Other 5974 3118 672
Formulate appropriate null and alternative hypotheses.
(M1 – the mean birth weight of babies of woman who tested positive,<br>M2 – the mean birth weight of babies of woman who either tested negative or were not tested)
a. Ho: M1 is not equal to M2.
Ha: M1 is equal to M2.
b. Ho: M1 is equal to M2.
Ha: M1 is not equal to M2.
c. Ho: M1 is greater than M2.
Ha: M1 is equal to M2.
d. Ho: M1 is equal to M2.
Ha: M1 is less than M2.
e. Ho: M1 is less than M2.
Ha: M1 is equal to M2.
Answer:
(d) Ho: M1 is equal to M2.
Ha: M1 is less than M2.
7. (Points: 2)
For the problem in question 6 find the value of the test statistic. Assume that the standard deviation for both populations is the same and use the pooled variance.
a. -6.57
b. -3.42
c. -1.45
d. 1.45
e. 3.42
f. 6.57
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Answer:
8. (Points: 2)
For the problem in question 6 find the P-value of the test.
a. -0.123
b. 0
c. 0.123
d. 0.367
e. 0.582
f. 1.34
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10. (Points: 1.5)
For the problem in question 6 give a left endpoint (lover limit, lower boundary) of the 95% confidence interval fo the mean difference (M1 – M2) in birth weights.
(M1 – the mean birth weight of babies of woman who tested positive,
M2 – the mean birth weight of babies of woman who either tested negative or were not tested)
a. – 543.15
b. -488.79
c. -385.67
d. -281.21
e. -126.41
f. 126.41
g. 281.21
h. 385.67
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11. (Points: 1.5)
For the problem in question 6 give a right endpoint (upper limit, upper boundary) of the 95% confidence interval for the mean difference (M1 – M2) in birth weights.
(M1 – the mean birth weight of babies of woman who tested positive,
M2 – the mean birth weight of babies of woman who either tested negative or were not tested)
a. – 543.15
b. -488.79
c. -385.67
d. -281.21
e. -126.41
f. 126.41
g. 281.21
h. 385.67
Bring to mind a real-world situation or problem that could be addressed using a one-way analysis of variance (ANOVA). You will not need SPSS to complete this Discussion question.
For this situation or problem:
Clearly identify the independent and dependent variables you would study, including the number of levels of the independent variable.
Generate the statistical null and alternative hypotheses.
Describe what information the effect size would tell you that the probability value would not tell you.
Explain what additional information confidence intervals around means (or around mean differences) would give your reader.
Explain when would you need to report a post hoc test and why.
Using realistic numbers for values of degrees of freedom, sample size, F-ratio, and confidence interval(s) (if appropriate), and post hoc results (if appropriate), report hypothetical results in a few sentences using correct APA format.
4. Explain why t distribution tends to be flatter and more spread than the normal distribution.
12. Last fall, a sample of n = 36 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshmen class. All freshmen must take the same English Languages Skills course, and the mean score on the final exam for the entire freshmen class was µ =74. The students in the new program has a mean score of M =79 .4 with a standard deviation of s =18
a. On the basis of these data, can the college conclude that the students in the new program performed significantly better than the rest of the freshmen class? Use a one-tailed test with ± = .05.
b. Can the college conclude that the students in the new program are significantly different from the rest of freshmen class? Use a two-tailed test with ± = .05.
16. In a classic study of infant attachment, Harlow (1959) placed infant monkeys in cages with two artificial surrogate mother. One â??mother was made from bare wire mesh and contained a baby bottle which the bottle from infants could feed. He other mother was made from soft terry cloth and did not provide any access to food. Harlow observed the infants and recorded how much time per day was spent with each mother. In a typical day, the infant spent a total of 18 hours clinging to one of the two mothers. If there were no preference between the two, you would expect the time to be divided evenly, with an average of µ =9 hours for each of the mothers. However, the typical hours monkey spent around 15 hours per day with the terry cloth mother, indicating a strong preference for the soft, cuddly mother. Suppose a sample on n = 9 infant monkeys averaged M = 15.3 hours per day with SS = 216 with the terry mother. Is this result sufficient to conclude that the monkeys spent significantly more time with the softer mother than would be expected if there were no preference? Use a two-tailed test with ± =.05.
22. A researcher would like to examine the effects of humidity on eating behavior. It is known that laboratory rats normally eat an average of µ= 21grams of food each day. He researcher selects a random of n =16 and places them in controlled atmosphere room in which the relative humidity is maintained at 90%. The daily food consumption scores for the rats are as follows:
a. Can the researcher conclude that humidity has a significant effect on eating behavior? Use a two-tailed test with ± =.05.
b. Compute the estimated d and r2 to measure the size of the treatment effect.
Gravel has been ordered from Lo Tran by Ace Construction The Lo Tran trucks carry 3 tons max per load. The costs per ton per truck to move gravel between sites is listed below. What are the optimum loads, routings, and costs of addressing this contract?
[Please see the attached questions file.]
1. Suppose you have drawn a simple random sample of 400 students from University X and recorded how much money each student spent on text books in Fall 2009. For your sample, sample mean (X-bar) is $500, and sample standard deviation (s) is $100. Construct a 99% confidence interval for the mean.
2. Suppose you have drawn a simple random sample of 400 students from University X. In this sample, 100 students own Blackberries. Let p denote the proportion of University X students who own Blackberries. Construct a 99% confidence interval for p.
3. Suppose you want to use a simple random sample to determine, within ± $20 and at a 99% level of confidence, the average amount of money a Syracuse University undergraduate student spends on text books in a year. If you know that the standard deviation is 100, compute the sample size you need.
4. Let m denote the average amount of money a household in County X spent on automobile insurance in 2009. You want to use a simple random sample to determine m within ±0.06 m at a 99% level of confidence. You have no prior idea of m. However, you expect that the amount a household spends on automobile insurance is roughly proportional to the annual income of the household. Also, from secondary data, you know that the mean annual income of County X was $75,000, and the standard deviation in annual income in County X was $30,000. Compute the sample size you need.
5. There are 150,000 full time college students in State X. You want to use a simple random sample to determine, within ± 6000 and with 99% confidence, how many of these 150,000 students own Blackberries. If you have no prior idea of how many, determine the sample size you need.
6. Suppose you want to study the population of full-time college students in State X. In this state, there are 150,000 full-time college students. Out of these students, 30,000 students study at private schools, and the other 120,000 students study at state schools. You have drawn a stratified sample using private school students and state school students as the two strata. For each student selected, you recorded how much money the student spent on tuition and other college expenses (expense) in 2009. The results are as follows:
(1) Private School Students: n1 = 100, X-bar-1 = 30,000, s1 = 15, 000.
(2) State School Students: n2= 400, X-bar-2 = 15,000, s2= 6000.
6. (a) Construct a 99% confidence interval for the total expense by all the 30,000 private school students, combined, in 2009.
6. (b) Let m denote the mean expense of a full-time college student in State X in 2009. Construct a 99% confidence interval for m.
7. In State X, there are 150,000 full-time college students. Out of these students, 30,000 students study at private schools, and the other 120,000 students study at state schools. You have drawn a stratified sample using private school students and state school students as the two strata and, for each student, recorded if the student owns an Apple computer.
Results:
(1) Private School Students: n1 = 100. In this sample of 100, 30 students own Apple computers.
(2) State School Students: n2 = 400. In this sample of 400, 80 students own Apple computers.
Let p denote the proportion of the overall full-time college student population in State X that own Apple computers. Construct a 99% confidence interval for p.
Problem 2
Acme Tires manufactures two types of tires: high performance tires and all weather tires. 45% of the tires they produce are high performance tires. They offer a 40,000 mile warrantee on each of the tires they sell, and 89% of all tires exceed 40,000 miles of tread life. Furthermore, 37% of all the tires sold are both all high performance tires AND exceed 40,000 of tread life. You can find this information filled out in the contingency table in tiressu10.xlsx. Use this information to answer the following questions. Questions 2.1 and 2.2 relate to information from week 4 in the class, 2.3 comes from week 5 material, and 2.4 is based on material from week 6. Note that part a (and ONLY part a) of question 2.3 is an extra credit question. Should you encounter any difficulties with these problems, the optional problems below are very similar to the questions in this problem set, and the answers to the optional questions can be found in the back of the textbook. You can also request that the tutor work extensively with you on the optional problems.
Problem 2.1
Use probability theory to answer the following questions:
(a) Give an example (related to the setting of the question) of a simple event.
(b) Give an example (related to the setting of the question) of a joint event.
(c) Use the information given to complete the contingency table.
(d) What is the probability that a tire selected at random is an all weather tire?
(e) What is the probability that a tire selected at random fails to last for 40,000 miles?
(f) What is the probability that a tire selected at random is either a high performance tire or fails to last for 40,000 miles?
(g) What is the probability that a tire selected at random is both an all weather tire and exceeds 40,000 miles of tread life?
(h) What is the probability that an all weather tire selected at random exceeds 40,000 miles of tread life?
(i) What is the probability that a high performance tire selected at random exceeds 40,000 miles of tread life?
Problem 2.2
Assume that Acme Tires sells their high performance tires for $220 each and their all weather tires for $140 each. Further assume that the cost of producing a high performance tire is $180 and the cost of producing an all weather tire is $125. Finally, assume that if a tire does not last 40,000 miles, Acme tires will replace it free of charge to the consumer; Acme will incur the cost of replacement, but will not receive any additional revenue.
(a) Calculate the profit earned/loss incurred on; a high performance tire that exceeds 40,000 miles, a high performance tire that does not exceed 40,000 miles, an all weather tire that exceeds 40,000 miles, and an all weather tire that fails to last 40,000 miles.
(b) What is the expected value (expected profit) of producing an all weather tire? Of producing a high performance tire?
(c) What is the variance and standard deviation of producing an all weather tire? Of producing a high performance tire?
Problem 2.3
Assume that Acme tire life is normally distributed and that both all weather tires and high performance tires have have a mean life of 50,000 miles. Furthermore, the standard deviation of tire life for all weather tires is 6,241.06 miles and the standard deviation of tire life for high performance tires is 10,824.07 miles.
(a) EXTRA CREDIT-Using the probabilities you calculated in problem 2.1, show that the numbers given here for the standard deviation of each tire type are correct. Note: depending on rounding, the numbers you calculate may be slightly higher or lower than the ones given in the problem.
(b) If Acme wanted to ensure that 95% of their tires exceeded the warrantee, what would they have to set their warrantee at for all weather tires? For high performance tires?
Excel Tips:
Excel has a trio of built in functions that are useful for calculating Z scores and dealing with the standard normal distribution. These are =STANDARDIZE, =NORMSINV, and =NORMSDIST. See the Excel helpfile for details on how to use these functions
Problem 2.4
In problem 2.3, you were given mean tire life and standard deviations of tire life for each tire type. Use this information to calculate:
(a) The probability that a sample of 16 all weather tires will have an average tire life of more than 52,000 miles.
(b) The probability that a sample of 64 all weather tires will have an average life of more than 52,000 miles.
(c) The probability that a sample of 5 high performance tires will have an average life of less than 40,000 miles.
(d) The probability that a sample of 20 high performance tires will have an average life of less than 40,000 miles.
Please answer 12.7(e)
e. State the conclusion of the test in part (d).
Review of the previous exercise and answers:
12.1 A manufacturer of industrial chemicals investigates the effects on its sales of promotion activities (primarily direct contact and trade show), direct development expenditures, and short-range research effort. Data are assembled for 24 quarters (6 years) and analyzed by Minitab as shown (in $100,000 per quarter).
Regression Analysis: Sales versus Promotion, Development, Research.
The regression equation is:
Sales = 326 + 136 Promotion – 61.2 Development – 43.7 Research
Predictor Coef SE Coef T P
Constant 326.4 241.6 1.35 0.192
Promotion 136.1 28.11 4.84 0.000
Development -61.18 50.94 -1.20 0.244
Research -43.70 48.32 -0.90 0.377
S = 25.6282 R-Sq = 77.0% R-Sq (adj) = 73.5%
Analysis of Variance
Source DF SS MS F P
Regression 3 43902 14634 22.28 0.000
Residual Error 20 13136 657
Total 23 57038
a. Write the estimated regression equation.
Sales = 326 + 136 Promotion – 61.2 Development – 43.7 Research
b. Locate MS(Residual) and its square root, the residual standard deviation.
MS (Residual) = 657 and its square root = 25.63.
c. Locate SS (Residual) and the coefficient of determination R2.
The SS (Residual) = 13136 and the coefficient of determination R2 = 77.0%.
12.2 State the interpretation of ?1, the estimated coefficient of promotion expense, of Exercise 12.1.
Coefficient of promotion expense is 136.1
This means sales increase by $136.11 * 100000 = $136110000 for every one million dollar more spent on promotion
12.7 Refer to Minitab computer output of Exercise 12.1
a. Locate the F statistic.
The F statistic = 22.28
b. Can the hypothesis of no overall predictive value be rejected at ± = .01?
p- value for the F- test is 0. This means at least one of the three predictor variables is significant in the regression.
Therefore, the hypothesis of no overall predictive value can be rejected at a = 0.01.
c. Locate the t statistic for the coefficient of promotion ?1.
T = 4.84
d. Test the research hypothesis that ?1 â? 0. Use ± = .05.
Since p- value for promotion expense is 0, we reject the hypothesis that the coefficient is 0, and conclude that promotion expense is a significant predictor of sales.
e. State the conclusion of the test in part (d).
1. Last year, at Northern Manufacturing Company, 200 people had colds during the year. One hundred fifty-five people who did no exercising had colds, while the remainder of the people with colds were involved in a weekly exercise program. Half of the 1,000 employees were involved in some type of exercise.
a. What is the probability that an employee will have a cold next year?
b. Given that an employee is involved in an exercise program, what is the probability that he or she will get a cold?
c. What is the probability that an employee that is not involved in an exercise program will get a cold next year?
d. Are exercising and getting a cold independent events? Explain your answer.
2. Fast Service Store has maintained daily sales records on the various size “Cool Drink” sales. These are shown in the following table:
“Cool Drink” Price Number Sold
$0.25 75
$0.35 120
$0.50 125
$0.75 50
a. Set up a probability distribution for “Cool Drink” sales.
b. What is the expected value of this probability distribution?
3. Martin Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspection procedure is to select 6 items, and if there are 0 or 1 defective cases in the group of 6, the process is said to be in control. If the number of defects is more than 1, the process is out of control. Suppose that the true proportion of defective items is 0.15.
a. What is the probability that there will be 0 or 1 defects in a sample of 6 (i.e., that the process is in control)?
b. What is the probability that there will be more than 1 defect in a sample of size 6 (i.e., that the process is out of control)?
c. What is the probability that there will be exactly 2 defects in a sample of size 6?
5. A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.
a. Assuming the company’s claim is true, if one home is selected at random, what is the probability that it will be sold in less than 63 days?
b. Assuming the company’s claim is true, if a random sample of 9 homes is selected, what is the probability that the mean selling time will be less than 63 days?
c. Assuming the company’s claim is true, if a random sample of 64 homes is selected, there is a 75% probability that the sample mean is greater than how many days?
d. Do you have to know that selling times are normally distributed to answer part (c)? Explain why or why not.
e. Suppose you doubt the company’s claim that their average selling time is 57 days. To test their claim, you select a random sample of 64 homes and the sample mean number of days to sell those homes is 62 days. Do you have evidence to refute the company’s claim? Explain why or why not.
7. The start of the twenty-first century saw many corporate scandals and many individuals losing faith in business. In a 2007 poll conducted by the New York City-based Edelman Public Relations firm, 57% of respondents say they trust business to “do what is right.” This percentage was the highest in the annual survey since 2001.
a. If the sample size is 100, construct a 95% confidence interval estimate of the population proportion of individuals who trust business to “do what is right.”
b. If the sample size is 200, construct a 95% confidence interval estimate of the population proportion of individuals who trust business to “do what is right.”
c. Based on the results of part (a), can you conclude that more than half of the respondents trust business to “do what is right”? Explain your answer.
d. Based on the results of part (b), can you conclude that more than half of the respondents trust business to “do what is right”? Explain your answer.
e. Discuss the effect that sample size has on the width of confidence intervals.
8. Suppose that it is a presidential election year and Ohio is one of the “swing” states. Your polling company wants to conduct a presidential preference poll of the citizens of Ohio to predict which candidate will win the election.
a. How many voters must be polled to be 95% confident of your results within +/- 3%?
b. How many voters must be polled to be 95% confident of your results within +/- 2%?
c. How many voters must be polled to be 95% confident of your results within +/- 1%?
d. Discuss the effect of margin of error on sample size.
2. The production department of NDB Electronics wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, two employees were assigned to assemble the subassemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 during a one-hour period. The complete set of paired observations follows.
The dependent variable is production; that is, it is assumed that the level of production depends upon the number of employees.
a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the
number of assemblers and production? Explain.
c. Compute the coefficient of correlation.
d. Evaluate the strength of the relationship by computing the coefficient of determination.
[See thee attached question file.]
Please calculate and answer this question step by step.
1. The owner of Maumee Ford-Mercury wants to study the relationship between the age of a
car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership
during the last year.
a. If we want to estimate selling price on the basis of the age of the car, which variable is
the dependent variable and which is the independent variable?
b. Draw a scatter diagram.
c. Determine the coefficient of correlation.
d. Determine the coefficient of determination.
e. Interpret these statistical measures. Does it surprise you that the relationship is inverse?
The UN must evacuate an aid team and their belongings from Iraq. They can hire two types of planes to handle the evacuation. One is an Airbus 201 which can handle 25 passengers and 10 tons of cargo for $800 per day. The other is a Boeing 179 which can handle 40 passengers and 4 tons of cargo at a cost of $1000 per day. The evacuation must take out at least 2000 personnel and at least 440 tons of belongings. How many of each type of plane should be chartered to minimize the cost per day and what is that minimum cost per day?
1. Solve the problem graphically.
2. Solve the problem using Solver (under Tools in Excel).
3. Solve the problem using QM for Windows.
4. What is the additional cost if you need to take out 1 additional last minute passenger?
These are non-statistical testing questions For each, identify the hypotheses, define Type I and Type II errors, and discuss the consequences of each error. In setting up the hypotheses, you will have to consider where to place the “burden of proof”
11.1 It is the responsibility of the federal government to judge the safety and effectiveness of new drugs. There are two possible decisions: approve the drug or disapprove the drug.
H0 :
H1 :
Workers in an industry earn $17.35 per hour on the average; the standard deviation is $2.10 per hour. If a sample of 40 workers is taken, how likely is it the mean will be:
a. Between $16.80 and $17.00?
b. Above $17.22?
Please use the attachments provided and not only excel functions.
A statistics instructor, wishes to study the relationship between the number of absences students have and their final course grades. The data obtained for o randomly selected statistics students is given below:… (Please see attached files)
(a) Find the equation of the linear regression line.
(b) What is the predicted final course grade for a students who was absent 5 imes using the linear regression equation
Prepare a word file solution to Q5. The summary output to Q5 is given in Excel file.
Chapter 9, Section 2
Problem 12
Interpreting Displays – Conduct the hypothesis test by using the results from the given displays.
Bednets to Reduce Malaria – In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaira. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria (based on data from Sustainability of Reductions in Malaria Transmission and Infant Mortality in Western Kenya with Use of Insecticide-Treated Bednets,” by Lindblade, et al., Journal of the American Medical Association, Vol. 291, No. 21). Use a 0.01 significance level to test the claim that the incidence of malaria is lower or infants using bednets. Do the bednets appear to be effective?
MINITAB
Difference = p (1) – p (2)
Estimate for difference: -0.00125315
99% Upper bound for difference: -0.00125315
Test for difference = 0 (vs < 0): z = -2.44 P-value == 0.007
Problem 38
Equivalence of Hypothesis Test and Confidence Interval – Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2000 people with 1404 of them having the same common attribute. Compare the results from a hypothesis test of p1 = p2 (with a 0.05 significance level) and a 95% confidence interval estimate of p1 – p2.
Chapter 9, Section 3
Problem 18
Assume that the two samples are independent simple random samples selected from normally distrubted populations. Do not assume that th epopulation standard deviations are equal, unless your instructor stipulates otherwise.
Hypothesis Test for Braking Distances of Cars – Refer to the sample data given in Exercise 17 and use a 0.05 significance level to test the claim that the mean braking distance of four-cylinder cars is greater than the mean braking distance of six-cylinder cars.
Exercise 17 – Sample Data
A simple random sample of 13 four-cylinder cars is obtained, and the braking distances are measured. The mean braking distance is 137.5 ft and the standarad deviation is 5.8 ft. A simple random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of 136.3 ft with a standard deviation of 9.7 ft (based on Data Set 16 in Appendix b ).
Problem 30
Radiation in Baby Teeth – Listed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvantia residents and New York residents born after 1979 (based on data from “Au Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s,” by Mangano, et al., Science of the Total Environment).
a. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from Pennsylvania residents is greater than the mean amount from New York residents.
b. Construct a 90% confidence interval of the difference between the mean amount of strontium-90 from Pennsylvania residents and the mean amount from New York residents.
Pennsylvania: 155 142 149 130 151 163 151 142 156 133 138 161
New York: 133 140 142 131 134 129 128 140 140 140 137 143
Chapter 9, Section 4
Problem 12
Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal.
Are Flights Cheaper When Scheduled Earlier? – Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.01 significance level to test the claim that flights scheduled one day in advance cost more than flights scheduled 30 days in advance. What strategy appears to be effective in saving money when flying?
Flight scheduled one day in advance 456 614 628 1088 943 567 536
Flight scheduled 30 days in advance 244 260 264 264 278 318 280
Problem 20
Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal.
Heights of Winners and Runners-Up – Listed below are the heights (in inches) of candidates who won presidential elections and the heights of the candidates who were runners up. The data are in chronological order, so the corresponding heights from the two lists are matched. For candidates who won more than once, only the heights from the first election are included, and no elections before 1900 are included.
a. A well-known theory is that winning candidates tend to be taller than the corresponding losing candidates. Use a 0.05 significance level to test that theory. Does height appear to be an important factor in winning the presidency?
b. If you plan to test the claim in part (a) by using a confidence interval, what confidence level should be used? Construct a confidence interval using that confidence level, then interpret the result.
Won Presidency Runner-Up
71 74.5 74 73 69.5 71.5 75 72 73 74 68 69.5 72 71 72 71.5
70.5 69 74 70 71 72 70 67 70 68 71 72 70 72 72 72
Chapter 9, Section 5
Problem 10
Hypothesis Tests of Claims About Variation – Test the given claim. Assume that both samples are independent simple random samples from populations having normal distributions.
Braking Distances of Cars – A random sample of 13 four-cylinder cars is obtained, and the braking distances are measured and found to have a mean of 137.5 ft and a standard deviation of 5.8 ft. A random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of 136.3 ft and a standard deviation of 9.7 ft (based on Data Set 16 in Appendix B). Use a 0.05 significance level to test the claim that braking distances of four-cylinder cars and breaking distances of six-cylinder cars have the same standard deviation.
Problem 16
Hypothesis Tests of Claims About Variation – Test the given claim. Assume that both samples are independent simple random samples from populations having normal distributions.
BMI for Miss America – Listed below are body mass indexes (BMI) for Miss America winners from two different time periods. Use a 0.05 significance level to test the calim that winners from both time periods have BMI values with the same amount of variation.
BMI (from recent winners): 19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8
BMI (from the 1920s and 1930s): 20.4 21.9 22.1 22.3 20.3 18.8 18.9 19.4 18.4 19.1
The fill amount of bottles of soft drink has been found to be normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liter. What proportion of the bottles contain
a. between 1.90 and 2.10 liters?
b. below 1.92 liters?
Please use the attachments provided and not only excel functions.
[See the Attached Questions File.]
Medical Blood Plasma. Let x be the variable that represents the pH of the arterial plasma (i.e. acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4. A new drug for arthritis has been developed. However it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis too the drug for 3 months. Blood tests show the average pH to be xbar = 8.1 with a sample standard deviation s = 1.9. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of blood.
The amount of time a bank teller spends with each customer has a population mean µ = 3.10 minutes and a standard deviation σ = 0.60. If a random sample of 36 customers is selected,
a. What is the probability that the average time will be at least 3 minutes?
b. What is the probability the average time will be between 3.05 and 3.2 minutes?
Please use the attachments provided and not only excel functions.
1. Contrast the phrases “mean of differences” and “difference of means”. Which phrase is appropriate for which t-test?
2. A sample of n = 16 scores has a mean of M = 83 and a standard deviation of s = 12.
a. Explain what is measured by the sample standard deviation.
b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error.
3. To evaluate the effect of a treatment, a sample of n = 9 individuals is obtained from a population with a mean of u = 40, and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33.
a. If the sample standard deviation is s = 9, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?
b. If the sample standard deviation is s= 15, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with x = .05?
4. Two separate samples receive two different treatments. One sample has n = 9 scores with SS = 710 and a second sample has n = 6 scores with SS = 460.
a. Calculate the pooled variance for the two samples.
b. Calculate the estimated standard error for the sample mean difference.
c. If the sample mean difference is 10 points, is this enough to reject the null hypothesis for a two-tailed test with x = .05?
d. If the sample mean difference is 13 points, is this enough to reject the null hypothesis for a two-tailed test with x = .05?
1 Explain the Central limit theorem in your own words. What is the value of it? What assumption does one have to make when using it?
2 You have a process that has a Mean of 22.5 and a standard deviation of 5.5, taken from a sample survey of n = 25. Produce a 90% confidence interval. Produce a 99% confidence interval. Compare the 2 intervals to each other and, in your own words explain the difference, in use of the two.
3 You took a survey on average time from submission of federal income tax using a computer based application and the person E-filed. The average time was 14.5 days with a 4.8 day standard deviation. The data came from a survey of 22 people contacted, randomly. Construct a 95% confidence interval. The federal government asserts that, from date of file to the recipient’s receipt of refund averages 11 days. Agree or Disagree and why?
This exercise is a “what if analysis” designed to determine what happens to the test statistics and interval estimates when elements of the statistical inference change. This can be solved manually or on Excel with Test statistics or Estimators workbook.
Random samples from two normal populations produced the following statistics:
S2 over1 = 350 n1 = 30 S2 over 2 = 700 n2 = 30
a) Can we infer at the 5% significance level that the two population variances differ?
b) Repeat part a changing the sample sizes to n1 = 15 and n2 = 15.
c) Describe what happens to the test statistic when the sample sizes decrease.
You are a quality analyst with John and Sons Company. Your company manufactures fax machines, copiers, and printers that use plain paper. The CEO of the company wants the machines to handle 99.5 percent of all the paper that is used in them without the paper getting jammed.
The CEO asks you to determine the thickness of paper that the machines must be able to handle to achieve this target. Using the data provided (at the bottom) , prepare a memo to the CEO in a Word document, detailing the appropriate confidence limits for the thickness of paper that the machines must be able to handle.
0.00399
0.00424
0.00375
0.00449
0.00422
0.00407
0.00434
0.00381
0.00421
0.00397
0.00425
0.00449
0.00462
0.00467
0.00404
0.00391
0.00431
0.00398
0.00415
What is the relationship between the variance and the standard deviation?
Why is the unbiased estimator of variance used?
The solution addresses the following:
1. During a cold winter, the temperatures stayed below zero for ten days. The range was -20 to -5. The variance of the temperatures of this period:
2. If the mean of a normal distribution is negative:
3. A 95% confidence interval for the mean weight (in ounces) of all apples from an orchard is (7.81, 9.23). Which of the following is not suggested as the value of the mean weight of all the apples?
4. Your firm has a contract to make 1000 staff uniforms for a fast -food retailer. The heights of the staff are normally distributed with a mean of 69 inches and a standard deviation of 2 inches. What percentage of uniforms will have to fit staff shorter than 67 inches? What percentage will have to be suitable for staff taller than 73 inches.?
The following data represent scores of 50 students in an applied business statistics test.
72 72 93 70 59 78 74 65 73 80
57 67 72 57 83 76 74 56 68 67
74 76 79 72 61 72 73 76 67 49
71 53 67 65 100 83 69 61 72 68
65 51 75 68 75 66 77 61 64 74
a. Prepare the frequency distribution table and the frequency histogram for this data set.
b. Compute the sample mean, sample median X(M), sample range, and sample variance.
c. Does the data set represent a sample or a population? If it is a sample, describe the population from which it has been drawn.
Hypothesis Testing
1. The MBA department is concerned that dual degree students may be receiving lower grades than the regular MBA students. Two independent random samples have been selected 450 observations from population 1 (dual degree students) and 410 from population 2 (MBA students). The sample means obtained are X1(bar) =84 and X2(bar) =86. It is known from previous studies that the population variances are 4.6 and 5.0 respectively. Using a level of significance of .05, is there evidence that the dual degree students are receiving lower grades? Fully explain your answer.
Simple Regression
2. A CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called DIB and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.
The use of linear regression is a critical tool for a manager’s decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows:
Month Advertising Cost (thousands of dollars) Number of Orders
1 $68.93 2,902,000
2 72.62 3,893,000
3 79.58 3,299,000
4 58.67 2,130,000
5 69.18 3,367,000
6 70.14 4,111,000
7 93.37 4,923,000
8 78.88 4,935,000
9 82.99 5,276,000
10 75.23 3,654,000
11 91.38 4,598,000
12 52.90 2,967,000
13 61.27 2,999,000
14 89.19 4,345,000
15 90.03 4,934,000
16 78.21 3,653,000
17 83.77 5,625,000
18 82.53 5,978,000
19 98.76 5,999,000
20 72.64 5,834,000
a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatterplot can more easily be generated using the Chart procedure.
NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to go to Tools select Add-ins and then choose the 2 data toolpak options. The original Excel CD will be required for this installation. It should take about a minute.
b. Assuming there is a statistically significant relationship, use the least squares method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under Tools > Data Analysis to construct this equation.
c. Interpret the meaning of the slope, b1, in the regression equation.
d. Predict the monthly advertising cost when the number of orders is 5,000,000. (Hint: Be very careful with assigning the dependent variable for this problem)
e. Compute the coefficient of determination, r2, and interpret its meaning.
f. Compute the standard error of estimate, and interpret its meaning.
Hypothesis Testing on Multiple Populations
3. The Course Manager for AMBA 610 wants to use a new tutorial to teach the students about business ethics. As an experiment she randomly selected 15 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the faculty, AuthorGen Presentation created by the faculty, or a well known tutorial by the ABC company. After completing their assigned tutorial, the students are given a Business Ethics test. At the .10 significance level, can she conclude that there is a difference between how well the different tutorials work for the students?
Students Grades on the Business Ethics Test following the Tutorial
PowerPoint Tutorial AuthorGen Tutorial ABC Tutorial
98 79 65
85 86 73
91 72 78
87 82 96
98 91 97
Construct both an ungrouped and a grouped frequency distribution for the data given below:
142 145 147 151 137 141 145 137 140 138
151 140 151 149 144 146 142 139 142 150
Thirty percent of all customers who enter a store will make a purchase. Suppose that six customers enter the store and that these customers make independent purchase decisions.
(a) Let x = the number of six customers who will make a purchase. Write the binomial formula for this equation.
(b) Use the binomial formula to calculate:
1. The probability that exactly five customers make a purchase.
2. The probability that at least three customers make a purchase.
3. The probability that two or fewer customers make a purchase.
4. The probability that at least one customer makes a purchase.
See attached file for 5 problems.
One personality test available on the World Wide Web has a subsection designed to assess the “honesty” of the test-taker. After taking the test and seeing your score for this subsection, you’re interested in the mean score, , among the general population on this subsection. The website reports that is , but you believe that differs from . You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is and that the standard deviation of their scores is …
A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. One hundred fifty bulbs are selected at random, and their mean lifetime is found to be months. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from months?
Perform a two-tailed test. Then fill in the table below…
The General Social Survey is an annual survey given to a random selection of about adults in the United States. Among the many questions asked are “What is the highest level of education you’ve completed?” and “If you’re employed full-time, how many hours do you spend working at your job during a typical week?”
In a recent year, respondents answered both questions. The summary statistics are given in the chart below. ..
Depression and insomnia often go hand-in-hand, and sometimes it is unclear which of the two should be the primary subject of treatment in individuals suffering from insomnia. Mendoza & Company, a national pharmaceutical firm, has positioned itself as a specialist in the production of both antidepressants and sleeping pills. Mendoza’s current business model describes the following breakdown of America’s approximately million adults suffering from insomnia…
A manufacturer of summer clothing has generated the following regression model for forecasting the number of pairs of walking shorts (in hundreds of thousands) that will be sold during the next few quarters…
The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?
1. What method of data collection would you use to collect data for a study where a drug was given to 10 patients and a placebo to another group of 10 patients to determine if the drug has an effect on a patient’s illness
use sampling
take a census
perform an experiment
use a simulation
2. The chances of winning the California Lottery are 1 in 22 million. This statement describes
inferential statistics
descriptive statistics
3. The number of seats in a movie theater are
quantitative
qualitative
4. After polling every 8th graduate, a major university estimated the annual salary of its alumni to be $103,000. What sampling technique was used
random
stratified
convenience
cluster
systematic
5. A recent survey by a national women’s association showed that the average salary of 3500 of its 65,000 membership was $73,000. This number is a
parameter
statistic
6. Subjects in a sample, when properly selected, should possess
the same or similar characteristics as the population desired.
the same number of discrete variables as the population desired.
the same qualitative characteristics as the population desired.
confounding variables that differ from the population desired.
7. Suppose the variance is 64. Find the standard deviation
4096
46
4069
8
8. This data shows the temperatures on randomly chosen days during a summer class and the number of absences on those days. (temperature, number of absences) (72, 3), (85, 7), (91, 10), (90, 10), (88, 8), (98, 15), (75, 4), (100, 16), (80, 5)
Find the equation of the regression line for the given data
y = -0.4668x – 31.737
y = 31.737x – 0.4668
y = 0.4668x – 31.737
y = -31.737x + 0.4668
9. A multiple regression equation is y = -8.5 + 0.964a + 8.104b, where ‘a’ is a person’s age, ‘b’ is the person’s body fat percentage, and ‘y’ is the person’s lean mass percentage. Predict the lean mass for a person who is 27 years old and has a body fat percentage of 4.5%.
34.89
17.16
22.35
17.89
10. Interpret an r value of 0.11.
strong negative correlation
weak positive correlation
strong positive correlation
no correlation
11. Use this table to answer the questions.
Time (in minutes Frequency
20-24 8
25-29 14
30-34 23
35-39 10
40-44 17
1. Identify the class width.
2. Identify the midpoint of the first class.
3. Identify the class boundaries of the first class.
4. Give the relative frequency for each class.
12. The heights in inches of 18 randomly selected adult males in LA are listed as: 70, 69, 72, 57, 70, 66, 69, 73, 80, 68, 71, 68, 72, 67, 58, 74, 81, 72.
1. Display the data in a stem-and-leaf plot.
2. Find the mean.
3. Find the median.
4. Find the mode.
5. Find the range.
6. Find the variance.
7. Find the standard deviation.
State the value of the correct rejection region for α = 0.05
State the correct rejection region for α = 0.01
What should be the correct decision and conclusion when testing to determine if the production line is operating properly by allowing a 10% probability of committing a Type 1 error?
In an article about investment growth, Money magazine reported that drug stocks show powerful long-term trends and offer investors unparalleled potential for strong and steady gains. The federal Health Care Financing Administration supports this conclusion through its forecast that annual prescription drug expenditures will reach $366 billion by 2010, up from $117 billion in 2000. Many individuals age 65 and older rely heavily on prescription drugs. For this group, 82% take prescription drugs regularly, 55% take three or more prescriptions regularly, and 40% currently use five or more prescriptions prescriptions. In contrast, 49% of people under age 65 take prescriptions regularly, with 17% taking three or more prescriptions regularly and 28% using five or more prescriptions (Money, September 2001) The U.S. Census Bureau reports that of the 281,421,906 people in the United States, 34,991,753 are age 65 years and older (U.S. Census Bureau, Census 2000).
a. Determine the probability that a person in the United States is age 65 or older.
b. Determine the probability that a person takes prescription drugs regularly.
c. Determine the probability that a person is age 65 or older and takes five or more prescriptions.
d. Given that a person uses five or more prescriptions, determine the probability that the person is age 65 or older.
Decide whether you would use a personal interview, telephone survey, or self-administered questionnaire. Give your reasons.
A survey of the residents of a new subdivision on why they happened to select that area in which to live. You also wish to secure some information about what they like and do not like about life in the subdivision.
The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 63 pounds?
1. Suppose you have drawn a simple random sample of 10 students from a college campus and recorded how many hours each student surfed the internet during the first week of February, 2010.
Results:
Student: 1 2 3 4 5 6 7 8 9 10
Hours of Internet Surfing: 9 12 4 10 5 18 8 12 6 6
For this sample, compute (Xi), the sample average (X-bar), (Xi – X-bar)2, and the sample standard deviation (s).
2. Suppose the annual snowfall in a city is normally distributed with a mean of 80 inches and a standard deviation of 25 inches. Find the probability that in a given year, snowfall in the city would be between 60 and 100 inches (that is, within ± 20 of m = 80).
3. Let X denote the amount of money an SU student spends on books in a year. Assume that population mean is $800, and the population standard deviation is $125. Suppose you have drawn a simple random sample of size 400 from the SU student
population. Compute the probability that the sample mean (X) is between $790 and $810.
4. Suppose 20% of SU students own Apple computers, that is, p = 0.2. You have drawn a simple random sample of size 400 from this population. Let p denote the proportion of the sample that own Apple computers. Compute the probability that for your sample of 400 students, p will fall between 0.18 to 0.22 (i.e., within ±.02 of p = .2)
1. A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors …
2. An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period …
3. Plot the data on U.S. general aviation shipment …
…
[See the attached Question File.]
The manager of the Tee Shirt Emporium reports that the mean number of shirts sold per week is 1,210, with a standard deviation of 325. The distribution of sales follows the normal distribution. What is the likelihood of selecting a sample of 25 weeks and finding the sample mean to be 1,100 or less?
In the judicial case of United States vs. City of Chicago, discrimination was charged in a qualifying exam for the position of Fire Captain. In the table below Group A is a minority group and Group B is a Majority Group.
Passed Failed
Group A 10 14
Group B 417 145
A) If one of the test subjects is randomly selected, find the probability of getting someone who passed the exam.
B) Find the probability of randomly selecting one of the test subjects and getting someone who is in Group B or passed.
C) Find the probability of randomly selecting two different test subjects and finding that they are both in Group A.
D) Find the probability of randomly selecting one of the test subjects and getting someone who is in Group A and passed the exam.
E) Find the probability of getting someone who passed, given that the selected person is in Group A.
Based on the results above, can we make a probability argument that discrimination is present based on p = 0.05? Why or why not. I am not interested in theory here, only the impact of the probabilities above!
Suppose that we know that the average income in Malvern, PA is $30,000 and that the standard deviation is $2,000. Assume that household incomes in Malvern are normally distributed. Using the Empirical Rule, please provide the range of incomes that we can expect 68% of the data to lie within. What about 95% and 99.73%?
Assume that we have just learned that the population of Malvern is bimodal and not normally distributed. Using Chebychev’s Theorem, what percent of our population can we expect to lie within plus or minus two standard deviations? What percent of our population can we expect to lie within plus or minus three standard deviations?
What kind of differences do we see in the above distributions when we compare the Empirical Rule to Chebychev’s Theorem. Which approach provides more precision? Why can’t we use plus or minus one standard deviation with the Chebychev analysis?
1. Use Excel in 1(a)
The following data give the times in seconds between the incoming telephone calls to a medical practice in the time period from opening at 8am to 9am.
2 10 6 8 21 18 11 17
10 9 14 17 6 13 11 19
7 11 4 12 13 9 6 15
9 16 5 10 7 11 14 10
(a) Produce a clearly labelled frequency histogram and associated frequency table for this data on Excel using bin values of 4, 8, 12, etc. Describe the shape of the distribution of times shown in the histogram.
(b) From the histogram (i.e. without calculation, so you will need to explain your reasoning), give an estimate of the mean for this distribution. Provide an interpretation in context for this statistic.
(c) The standard deviation for this set of data is approximately 5 seconds. What does this tell you about the distribution of the data?
(d) In the period from 8am to 9am tomorrow, what proportion of the times between phone calls at this practice would you expect to be less than 16 seconds?
(e) This sample of times would not be representative of all times between phone calls for this medical practice. Why? Indicate how the data may be biased.
2. Use Excel in 2(a) and (d)
A study was conducted on the age at which infants learn to crawl. Twelve babies born at each of two
hospitals were monitored from birth by a child health nurse. The ages at which these infants learned to
crawl are recorded below in weeks.
Hospital A Hospital B
31.43 34.57 27.86 31.29 25 28.57 26.86 25.86
29.43 30.57 29.71 30.86 26.57 30.43 33.71 32.86
35.86 33.29 33.43 32.29 32.14 33.57 32.71 36
(a) Using the Excel boxplot macro from the Online Unit construct informative side-by-side boxplots for these sets of data. Edit the axis scale to start at 20 weeks.
(b) Compare the two sets of data in terms of their distribution characteristics – location, shape and spread.
(c) Using the boxplots and explaining your reasoning , what would you estimate as the proportion of all babies born at Hospital B who
(i) didn’t crawl until after the age of 33 weeks?
(ii) first crawled between 24 and 28 weeks?
(d) Calculate the coefficients of variation for the two sets of data using appropriate figures from Excel’s Descriptive Statistics. Comment on the meaning of your results.
Use Excel in this question.
3. The file WineSales.csv contains data on monthly Australian sales of sweet white wine, in thousands of litres, from January 1984 to July 1993.
(Source: Australian Bureau of Statistics, quoted by Hyndman, R.J. (n.d.) Time Series Data Library,
http://robjhyndman.com/TSDL. Accessed 28 Jan 2011)
(a) Provide a graphical display of the data that will be suitable for examining the changing trends in Australian sales of sweet white wine over this period.
(b) Outline any significant trends you observe in your graph, noting first the overall impression, and then providing more detailed descriptions.
(c) Describe any seasonal (short-term) variation in your graph and give a possible reason for it.
4. Use Excel in 4(b)
Consider the data SproutTemp.csv obtained on the growth process for beans sprouts, where the yield is related to the temperature. The rate at which the sprouts grow is measured by the time it takes a sprout to reach 4 cm. This time is recorded in the data file in days, together with the associated temperature in degrees Celsius.
(a) When performing a linear regression analysis on this data which of the two variables should be treated as the independent variable? Why?
(b) Produce full regressions statistics output from Excel, together with a well-presented, clearly labelled scatterplot of the data showing the least squares regression line.
(c) From your output, find the sample correlation coefficient between temperature and time taken for the sprouts to reach 4cm, and use it to comment on the type and strength of the linear relationship between the variables.
(d) State clearly the equation of the regression line. Use it to estimate the time taken for sprouts to reach 4cm when kept at a temperature of 15 ºC. (Is your estimate close to the actual value observed in the data corresponding to a temperature of 15 ºC?)
(e) Would this regression line be useful in predicting the growth time at 40 ºC? Why?
(f) “Less than 5% of the variation in growing times in this data set was not explained by the variation in temperature”. Comment on the accuracy of this statement with reference to the coefficient of determination for this regression analysis.
5. Government social services offered in a metropolitan area were classified in four divisions – aged care; family services; migrant assistance; and training facilities. Family services employed half of the social service workers in this area, 25% worked in aged care, and 10% with migrants. The remaining staff worked in training.
(a) For a survey, a consultant statistician wants to choose 120 social service staff to interview about workplace stress. Explain the type of sampling method you would recommend and how to implement it in this case.
(b) Last week 8% of the total social services staff in the area were absent, and 32% of these were from aged care. Use the information provided to answer the following:
(i) What is the probability that a social services staff member from this area does not work withmigrants or the aged?
(ii) What is the probability that a social services staff member was absent last week and was from aged care?
(iii) What percentage of the aged care staff were absent last week?
(iv) What is the chance that four randomly selected social service workers, from this metropolitan area, would all work in training facilities? Justify your answer.
The problem is to estimate that sales for the coming year for a maker of industrial equipment. The forecast is based on askingcustomers how much they are planning to order next year. To use the research budget efficiently, the customers are stratisifiedby the size of their orders during the past year. The following is some relevant information based on the past year”
Strata Customer Size Proportion Standard Deviation Interview Cost
Large 0.1 40 64
Medium 0.2 3 64
Small 0.7 2 64
Number of customers 5,000
A. Assume that a total of 300 interviews are to be conducted. How would you allocate those interviews among the three strata?
B. If a simple random sample of size 300 were obtained from the population, about 10 percent, or 30 interviews, would be from large customers stratum. Why did you recommend in part (a) that more than 30 interview be conducted from this stratum?
C. The survey was conducted, and the average values (in thousands) for each stratum were as follows:
X1=100
X2=8
X3=5
What would your estimate be of the population mean, the average sales that will be received from all customers next year?
D. Given the context of part ( c ) what would be the variance of your estimate of the population mean? Do you think that this variance would be larger or smaller than the variance of your estimate of the population mean if you had taken a simple random sample of size 300 from the total population? Why?
E. What is the total interviewing cost, given a cost per interview of $64, and 300 interviews?
F. Assume now that it has been decided that the small customers can be contacted by phone, making their cost per interview only $9 each. Repeat the analysis that you did in part ( a). How would you allocate 300 interviews now?
G. Now under part (f) what is the total interviewing cost?
H. How many interviews could you conduct, assuming that you had the same amount of money determined under part (e), that you allocated the interviews according to your answer in part (f) and that the costs were as in part (f)?
10.30 In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain Accident Rate for Dallas Fire Trucks
Statistic Red Fire Trucks Yellow Fire Trucks
Number of accidents x1 = 20 accidents x2 = 4 accidents
Number of fire runs n1 = 153,348 runs n2 = 135,035 runs
10.44 Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill. (a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value. Interpret the results at α = .01. (c) Is normality assured? (d) Is the difference large enough to be important? (e) What else would medical researchers need to know before prescribing this drug widely? (Data are from Science News 153 [May 30, 1998],
10.46 To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference at α = .05? (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value assuming equal variances. Interpret these results. (c) Is the difference in mean scores large enough to be important? (d) Is it reasonable to assume equal variances? (e) Carry out a formal test for equal variances at α = .05, showing all steps clearly.
10.56 A sample of 25 concession stand purchases at the October 22 matinee of Bride of Chucky showed a mean purchase of $5.29 with a standard deviation of $3.02. For the October 26 evening showing of the same movie, for a sample of 25 purchases the mean was $5.12 with a standard deviation of $2.14. The means appear to be very close, but not the variances. At α = .05, is there a difference in variances? Show all steps clearly, including an illustration of the decision rule.
11.24 In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Crash1
Crash Damage ($)
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1920
1. a – What determines an appropriate population?
b- What determines adequate sample size?
c- Please interpret: “….the study not be ‘too big’, where an effect of little scientific importance is nevertheless statistically detectable.” And explain.
2. Consider we have a survey. What if we have non-response to particular questions in the survey. What is the impact of this type of non-response to our research? (positive or negative, etc)
3. Consider “participants refuse to answer a certain survey questions during a interview process.”
What can we learn from this if anything?
4. Please define for sampling and explain the relationships among them:
a) Reliability
b) Validity
c) Accuracy
d) Precision.
1. A study of 35 golfers showed that their average score on a particular course was 92. The standard deviation of the population is 5.
A. Find the best point estimate of the mean.
B. Find the 95% confidence interval of the mean score for all golfers.
C. Find the 95% confidence interval of the mean score if a sample of 60 golfers is used instead of a sample of 35.
D. Which interval is smaller? Explain why.
2. A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large plain pizza. How large should the sample be if she wishes to be accurate to within $0.5? A previous study showed that the standard deviation of the price was $0.26.
3. A sample of six college wrestlers had an average weight of 276 pounds with a sample standard deviation of 12 pounds.
A. Find the 90% confidence interval of the true mean weight of all college wrestlers.
B. If a coach claimed that the average weight of wrestlers on the team is 310, would the claim be believable?
4. It has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field. A random sample of 400 incoming college freshmen was asked their preference, and 95 replied that they were considering business as a major.
A. Estimate the true proportion of freshman business majors with 98% confidence.
B. Does your interval contain 20.4?
5. Nearly one half of Americans aged 25 to 29 are unmarried. How large a sample is necessary to estimate the true proportion of unmarried Americans in this age group within 21/2 percentage points within 90% confidence?
Do academy awards involve age discrimination?
I. Test the hypothesis that the proportion of Actors over 40 years old who receive the award is different from the proportion of Actresses over 40 years old who receive the award. Show all steps of the hypothesis test.
II. Test the hypothesis that the mean age of all males is equal to the mean age of all females.
Show all steps in the process, use a significance level of 0.10 and then comment on whether the results fit your predictions when you compared the confidence intervals.
1. How many ways can an EMT union committee of 5 be chosen from 25 EMTs?
100
125
15,504
53,130
2. Which of the following cannot be a probability?
0
-49
0.001
14%
3. List the sample space of rolling a 6 sided die.
{1, 3, 5}
{1, 2, 4, 6}
{1, 2, 3, 4, 5, 6}
{2, 3, 4, 5, 6}
4. What is the probability of choosing a face card (jack, queen, or king) on the second draw if the first draw was a king (without replacement)?
0.231
0.784
0.216
0.769
5. A respiratory class has 33 women and 18 men. If a student is chosen randomly to be the team leader, what is the probability the student is a woman?
0.33
0.353
0.67
0.647
6. Compute the following: 3! ÷ (0! * 3!)
6
1
12
0
7. Decide whether the experiment is a binomial, Poisson, or neither based on the information given. You observe the gender of the next 950 babies born at a local hospital. The random variable represents the number of girls. Historically, 49.8% of the babies born are girls.
binomial
Poisson
neither
8. Given a Poisson distribution with mean = 4. Find P(X > 3).
0.195
0.238
0.433
0.567
9. Given the random variable X = {4, 5} with P(4) = 0.4 and P(5) = 0.6. Find E(X).
1.6
4.6
2.4
3.0
10. If X = {10, 20, 30, 40} and P(10) = 0.30, P(20) = 0.30, P(30) = 0.30, and P(40) = 0.30, can distribution of the random variable X be considered a probability distribution?
yes
no
11. If X = {2, 6, 10, 14} and P(2) = 0.2, P(6) = 0.3, P(10) = 0.4, and P(14) = 0.1, can distribution of the random variable X be considered a probability distribution?
yes
no
12. The weight of a box of Cheerios represents what kind of distribution?
discrete
continuous
13. Our baby’s weight represents what kind of distribution?
discrete
continuous
14. The number of patients donating blood in a day represents what kind of distribution?
discrete
continuous
15. We have a binomial experiment with p = 0.4 and n = 2.
a. Set up the probability distribution by showing all x values and their associated probabilities.
b. Compute the mean, variance, and standard deviation.
Some students were asked if they carry a credit card. Here are the responses.
[Please refer to the attachment for the data]
1. What is the probability that the student is a sophomore given he doesn’t carry a credit card?
2. What is the probability that the student was a freshman? (Points: 5)
3. What is the probability that the student is a freshman and doesn’t carry a credit card?
Last year the records of Dairy Land Inc., a convenience store chain, showed the mean amount spent by a
customer was $30. A sample of 40 transactions this month revealed the mean amount spent was $33 with
a standard deviation of $12. At the 0.05 significance level, can we conclude that the mean amount spent
has increased? What is the p-value? Follow the five-step hypothesis testing procedure.
The feasibility of constructing a profitable electricity-producing windmill depends on the mean velocity of the wind. For a certain type of windmill, the mean would have to exceed 20 miles per hour in order for its construction to be warranted. The determination of a site’s feasibility is a two stage process. In the first stage, readings of the wind velocity are taken and the mean is calculated. The test is designed to answer the question, Is the site feasible? In other words, is there sufficient evidence to conclude that the mean wind velocity exceeds 20 mph? If there is enough evidence, the site is removed from consideration. Discuss the consequences and potential costs of Type 1 and Type II errors.
Please see attached file for data required.
PC World provided ratings for 15 notebook PCs (PC World, February, 2000). The Performance Score is a measure of how fast a PC can run a mix of common business applications as compared to a baseline machine. For example, a PC with a performance score of 200 is twice as fast as the baseline machine. A 100-point scale was used to provide an overall rating for each notebook tested in the study. A score in the 90s is exceptional, while one in the 70s is good. The data for 15 notebook PCs are include in the following Chapter 3 dataset: PCs.
Based on your analysis of the data, write a managerial report addressing the following questions:
1. Write a paragraph describing the dataset. Identify the elements and variables, as well as the sample and population of interest. Identify the scale for each variable. Does the data represent time-series or cross-sectional data? Is it an experimental or observational study?
2. Construct a frequency distribution for the variable ‘Performance Score’ that includes frequency, relative frequency, and percent frequency. Represent the frequency distribution graphically using a bar graph or pie chart. Categories and percentages should be clearly labeled. You are responsible for determining the number of classes, class limits, and width of each class. Discuss what the frequency distribution tells us about the data.
3. Compute the mean, median, standard deviation, coefficient of variation, skew values, and 85th percentile for both variables included in the study. Which variable contains the most variation? What else do these descriptive statistics tell us about the data?
4. Compute the covariance and correlation coefficient for the relationship between Performance Score and Overall Rating. What does the correlation coefficient tell us about the relation between these two variables? Depict the relationship between the variables graphically using a scatterplot.
5. Assume that Performance Scores are normally distributed. What is the probability that a randomly selected notebook PC would have a performance score above 190? What is the probability that a randomly selected notebook PC would earn a performance score between 142 and 225?
An insurance company charges a 21 year old male a premium of $250 for a one year $100,000 life insurance policy. A 21 year old male has a 0.9985 probability of living for a year.
From the perspective of a 21 year old male (or his estate), what are the values of the two different outcomes
The value if he lives is $_______
The value if he dies is $_______
What is the expected value for a 21 year old male who buys the insurance
The expected value is $_______
What would be the cost of the insurance if the company just breaks even (in the long run with many such policies), instead of making a profit?
$______
A sociologist in interested in the relation between x = number of job changes and y = annual salary( in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information: ( You may have to re-write the graph below because I cannot get it to line up properly, I hope it does not confuse you, I actually re-typed it below, hopefully it will come out clearer:)
X # of Jobs| 4 7 5 6 1 5 9 10 10 3
Y $ in $1000| 33 37 34 32 32 38 43 37 40 33
Ex = 60; Ey = 359; Ex^2= 442; Ey^2= 13,013; Exy= 2231
A) draw a scatter diagram
B) find the equation of the least-squared line, and plot the line on the scatter diagram of part (a).
C) find the correlation coefficient of r. Find the coefficient determination of r^2. What percentage of variation in y in explained by the variation in x and the least-squares model?
D) if someone had x = 2 job changes, what does the least-squares line predict for y, the annual salary?
X ( # of jobs) Y ( salary in $1000)
4 33
7 37
5 34
6 32
1 32
5 38
9 43
10 37
10 40
3 33
Based on data from a car bumper sticker study, when a car is randomly selected, the number of bumber stickers and corresponding probabilities are shown below.
0 (0.794)
1 (0.099)
2 (0.041)
3 (0.015)
4 (0.014)
5 (0.012)
6 (0.008)
7 (0.006)
8 (0.006)
9 (0.005)
Does the given info describe a probability distribution? YES or NO
Assuming that a probability distribution is described, find the mean and standard deviation?
Mean = ______
Standard deviation = ______
Use the range rule of thumb to identify the range of values for unusual numbers of bumper stickers
Max unusual value = ______
Min unusual value = _______
A sale representative must visit 4 cities: Omaha, Dallas, Wichita, and Oklahoma City. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.
What are independent samples?
What is a pooled estimate of variance and why do you need to calculate it?
When do you use a dependent versus an independent sample t test?
Which is the more powerful t test?
What are the assumptions of the independent t test?
What are the mechanics of conducting an independent samples t test?
Young Professional magazine was developed for a target audience of recent college graduates who are in their first 10 years in a business career. In its two years of publication the magazine has been fairly successful. Now the publisher is interested in expanding the magazines advertising base. Potential advertisers continually ask about the demographics and interests of subscribers to Young Professional. To collect this information, the magazine commissioned a survey to develop a profile of its subscribers. The survey results will be used to help the magazine choose articles of interest and provide advertisers with a profile of subscribers. As a new employee of the magazine, you have been asked to help analyze the survey results.
Some of the survey questions follow:
What is your age?
Are you m/f?
Do you plan to make any real estate purchases in the next two years?
What is the approximate total value of financial investments?
How many stock/bond/ mutual fund transactions have you made in the last year?
Do you have broadband internet access?
What is your total household income?
Do you have any children?
1.) Develop 95% confidence intervals for the mean age and household income of subscribers
2.) Develop 95% confidence intervals for the proportion of subscribers who have broadband access at home and the proportion of subscribers who have children.
3.) Would Young Professional be a good advertising outlet for online brokers? Justify your conclusion with statistical data
4.) Would this magazine be a good place to advertise for companies selling educational software and computer games for young children
5.) Comment on the types of articles you believe would be of interest to readers of Young Professional.
[Please refer to the attachment for the data]
Sun Love grapefruit growers have determined that the diameters of their grapefruits are normally distrubuted with a mean of 4.5 inches and a standard deviation of 0.3 inches.
A) What is the probability that a randomly selected grapefruit will have a diameter of at least 4.14 inches?
B) What percentage of the grapefruits has a diameter between 4.8 and 5.04 inches?
C) Sun Love packs their largest grapefruits in special package called the super pack. If 5% of all their grapefuits are packed as super packs, what is the smallest diameter of the grapefruits that are in the super packs?
D) In this year harvest, there were 111,500 grapefruits that had a diameter over 5.01 inches. How many grapefruits has Sun Love harvested this year?
PROBLEM 1:
NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is $1.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, WI, area revealed that the mean price was $1.52 per gallon and that the standard deviation was $0.05 per gallon. At the .05 significance level, can we conclude that the price of gasoline is higher in the Milwaukee area? Calculate the p-value and interpret.
PROBLEM 2:
Suppose Babsie generated the
following probability distribution: X p(x)
____________________ ______
5 .25
7 .30
10 .25
12 .05
15 .15
a. Is this probability distribution discrete or continuous? Explain your reasoning.
b. Calculate the expected value of X. Show your work!!
c. Calculate the variance of X. Show your work!!!
d. Calculate the standard deviation. Show your work!!
PROBLEM 3:
Babsie is a public affairs specialist at Park University. A press release issued by Babsie based on some research claims that Park University students study at least as much as the national average for students at four year universities. Across the nation, 73 percent of all students at four year universities study at least four hours per week. Seventy percent of one hundred randomly selected Park University students surveyed claimed to study more than four hours per week. Should the University retract its previous statement? Explain why or why not. Answer using a 95 percent confidence interval.
PROBLEM 4:
The weights (in pounds) of a sample of five boxes being sent by UPS are: 12, 6, 7, 3, and 10.
a. Compute the mean for this sample. Show your work!!
b. Compute the range for this sample. Show your work!!
c. Compute the variance for this sample. Show your work!!
d. Compute the standard deviation for this sample. Show your work!!
SHORT ANSWER:
1. In hypothesis testing, what is a Type I error? Type II error?
2. List the characteristics of a normal distribution.
3. What is the difference between the Empirical Rule and Chebyshev’s rule?
4. In a standard normal distribution, what is the value of the mean and standard deviation?
The manufacturer of an airport baggage scanning machine claims it can handle an average of 580 bags per hour. At alpha (?) = .01, would a sample of 18 randomly chosen hours with a mean of 525 and a standard deviation of 45 support the manufacturer’s claim? Do both by hand and with Excel.
Note- Use a 0.05 level of significance unless otherwise stated and do by hand and excel.
Please answer True or False and explain why
1. For a normally distributed population of heights of 10,000 women, µ= 63 inches and ó = 5 inches. The number of heights in the population that fall between 66 and 68 inches is 1156.
2. In a normal distribution, approximately 91.31% of the area under the curve is found to the right of a point -1.36 standard deviations from the mean.
3. Approximately 92.5% of the area under the normal curve is located between the mean and +/- 1.78 standard deviations from the mean.
The retailing manager of a supermarket chain wants to determine whether product location has any effect on the sale of pet toys. Three different aisle locations are considered: front, middle, and rear. A random sample of 18 stores is selected, with 6 stores randomly assigned to each aisle location. The size of the display area and price of the product are constant for all stores. At the end of a one month trial period, the sales volumes (in thousands of dollars) of the product in each store were as follows:
Front Aisle Location: 8.6, 7.2, 5.4, 6.2, 5.0, 4.0
Middle Aisle Location: 3.2, 2.4, 2.0, 1.4, 1.8, 1.6
Rear Aisle Location: 4.6, 6.0, 4.0, 2.8, 2.2, 2.8
a. At the 0.05 level of significance, is there evidence of a significant difference in mean sales among the various aisle locations?
b. If appropriate, which aisle locations appear to differ significantly in mean sales?
c. n/a
d. What should the retailing manager conclude? Fully describe the retailing manager’s options with respect to aisle locations.
[See the attached Question file.]
Suppose a firm evaluates the productivity of the three shifts of workers who work in their factory. Each shift’s performance is measured on the amount of output that is produced during the shift – day, evening, or swing shift. Based on these ratings presented in the table below, produce an ANOVA analysis in Excel (see the example of a 1-way ANOVA in Course Materials), and determine if the average amount of output for any shift is different than the others.
Please show all calculations (especially the calculations of the variances for each shift (how the resultant variance number is derived), and also show the calculations how the P-value is determined – whether by formula or by charts.
Day Evening Swing
6 5 5
8 8 6
9 7 5
8 7 7
8 6 5
9 7 6
7 7 5
8 8 5
7 6 6
7 5 5
Compute the mean, mode, range, standard deviation, and variance from the following set of scores.
145; 210; 300; 178; 110; 237; 155; 187; 204; 205; 205; 287; 256; 200
Please refer to the attached Excel Sheets fo the data.
1. For the following variables, state what kind of measurement is being used? (Nominal, Ordinal, Interval, Ratio)
a. Geographic Region
b. Control
c. Payroll Expenditure
2. Create a frequency distribution for the ‘beds’ variable.
3. From that frequency distribution, make a histogram.
4. Using information from the first 8 hospitals in the dataset, make a pie chart for the ‘payroll expenditure’ variable.
5. Using information from the first 8 hospitals in the dataset, make a stem and leaf plot for the ‘personnel’ variable.
6. Looking at the graph from questions 4 and 5, can you spot a relationship between the two variables, ‘payroll’ and ‘personnel’? Explain.
7. Consider the data you used in questions 4 and 5 as “paired data”: each ‘payroll’ observation is accompanied by the ‘personnel number’ in an (x,y) pair. Generate a scatter plot of this paired information. Does this plot support your conclusions from question 6?
I needed some help or ideas for these questions:
1. Provide an example of each type of central tendency measurements: mean, median, and mode.
2. Calculate the Standard Deviation of the following numbers: 1, 3, 4, 6, 9, 19.
3. Go to the following website and complete the quiz on central tendency measurements, and then report your results and comment on any of the questions that you found challenging:
http://webquiz.ilrn.com/ilrn/quiz-public;jsessionid=54DEB5984B8056D2AB6C282F0AD3BCF7?name=stmr01q%2Fstmr01q_chp01&cookieTest=1
Comparing Variations:
1. For the following exercise, complete the following:
Find the mean, median, and range for each of the two data sets.
Find the standard deviation using the rule of thumb for each of the data sets.
Compare the two sets and describe what you discover.
The following data sets shows the ages of the first seven presidents (President Washington through President Jackson) and the seven most recent presidents including President Obama. Age is given at time of inauguration.
First 7: 57 61 57 57 58 57 61
Second 7: 61 52 69 64 46 54 47
2. A data set consists of a set of numerical values. Which, if any, of the following statements could be correct?
There is no mode.
There are two modes.
There are three modes.
3. Indicate whether the given statement could apply to a data set consisting of 1,000 values that are all different.
The 29th percentile is greater than the 30th percentile.
The median is greater than the first quartile.
The third quartile is greater than the first quartile.
The mean is equal to the median.
The range is zero.
Instructions: Use only the data meant for each question for your calculation.
(See attached file for full problem description)
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