Statistics: Hypothesis Testing

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 150 observations from population 1 (dual degree students) and 200 from population 2 (MBA students). The sample means obtained are X1(bar)=86 and X2(bar)=88. It is known from previous studies that the population variances are 4.8 and 5.2 respectively. Using a level of significance of .10, 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 3,902,000
2 72.62 3,893,000
3 79.58 5,299,000
4 58.67 4,130,000
5 69.18 4,367,000
6 70.14 3,111,000
7 93.37 3,923,000
8 68.88 4,935,000
9 82.99 5,276,000
10 75.23 4,654,000
11 91.38 4,598,000
12 52.90 2,967,000
13 61.27 3,999,000
14 79.19 4,345,000
15 90.03 3,934,000
16 78.21 4,653,000
17 83.77 5,625,000
18 62.53 3,978,000
19 98.76 4,999,000
20 72.64 3,834,000

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 tool pack 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 5,100,000. (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 .01 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
88 79 65
85 86 83
91 72 78
87 92 86
88 91 81

Statistics: Hypothesis Testing

The following table is given in an ANOVA test:

Treatment 1 Treatment 2 Treatment 3
9 13 10
7 20 9
11 14 15
9 13 14
12 15
10

The level of significance is 0.05. Answer only the following three parts.

a. How many degrees of freedom are there in the numerator?

b. How many degrees of freedom are there in the denominator?

c. What is the decision rule?

B. Complete the following:

The following is sample information. Test the hypothesis at the 0.05 level of significance the treatment means are equal.

Treatment 1 Treatment 2 Treatment 3
9 13 10
7 20 9
11 14 15
9 13 14
12 15
10

a. State the hypothesis.

b. State the decision rule.

c. Calculate the test statistic. Copy and paste your Excel or Megastat.

d. Make a decision.

C. Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level.

Treatment 1 Treatment 2 Treatment 3
8 3 11
11 12 20
10 11 18
8 12
4

a. Set up the null hypothesis and alternative hypothesis.

b. State the decision rule.

c. Use Excel or Megastat to complete an ANOVA table. Copy the table and paste it here, not as a separate attachment.

d. Accept or reject the null?

Statistics: Hypothesis Testing

A coin was flipped 100 times and came up heads 59 times and tails 41 times. The expected outcome was to land on heads or tails 50 times each. Do a hypothesis test to test the null that the percentage is equal to the expected as opposed to the alternative that it is greater or lesser or equal to the expected value, depending on the hypothesis.

Statistics: Hypothesis Testing

Questions:
1. When would you use a one- or two-sample hypothesis test? Provide examples.
2. What are the differences between dependent and independent samples? Provide examples.

Statistics: Hypothesis testing

2. A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the .10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

Pine trees Spruce trees
Sample size 40 70
Mean trunk diameter (cm) 45 39
Sample variance 100 150

A. The data does not support the claim because the test value 1.29 is greater than 1.28.
B. The data supports the claim because the test value 2.78 is greater than 1.28.
C. The data supports the claim because the test value 2.78 is greater than 1.64.
D. The data does not support the claim because the test value 1.29 is less than 1.64.

3. A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the variation of the amount of money spent on lunches. The variance of nine business dinners was $6.12 and the variance of 12 business lunches was $0.87. What is the test value?

A. 3.10
B. 9.61
C. 49.50
D. 7.03

Statistics: Hypothesis Testing

Environmental health indicators include air quality, water quality, and food quality. Twenty-five years ago, 47% of U.S. food samples contained pesticide residues. In a recent study, 44 of 125 food samples contained pesticide residues.

a. State the hypotheses that can be used to show that the population proportion declined.

b. What is the sample proportion?

c. What is the p-value?

d. Use a = .01. What is your conclusion?

Statistics: Hypothesis testing

Two different formulation of an oxygenated motor fuel are being used to study their road octane numbers. The variance of road octane number for formulation 1 is 1.5 and for formulation 2 is 1.2. The random sample size for formulation 1 is 15 and for formulation 2 is 20 are rested, both from normally distributed populations. The sample mean <x1>=89.6 and <x2>=92.5

a) If formulation 2 produce a higher road octane number than formulation 1, the manufacturer would like to detect it. Using significant level of 0.05 and formulate the null hypothesis and alternative hypothesis.
b) What is the test conclusion using critical value approach?
c) what is the p-value and test conclusion?

Statistics: Hypothesis Testing

Use the attached excel file which consists of 200 MBA students at Whatsamattu U. The file includes variables regarding students’ age, gender, major, GPA, Bachelors GPA, course load, English speaking status, family, weekly hours spent studying. Each of the three assigned problems should be formatted as a one page memo.

COMPLETE PROBLEM 1: The battle of the sexes lives on still today. Since admission standards do not address gender there should be an equally diverse group of men and women in school, but do they perform equally well? Using the sample of 200 students, conduct a hypothesis test for two independent samples to determine if the mean GPA differs for men and women. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart (a bar chart or column chart will probably work best) comparing the means of the two groups.

COMPLETE PROBLEM 2: You have heard that men are more likely than women to declare a major in an MBA program. Using the sample of 200 students (in the data file), conduct a hypothesis test of proportions to determine if the proportion of women with “no major” is greater than the proportion of men with “no major”. Use a .05 significance level. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart comparing the proportion of men without a major with the proportion of women without a major.

COMPLETE PROBLEM 3: You have probably heard that if you want something done, give it to a busy person. So is one’s employment status a factor in their academic performance? Using the sample of 200 students (in the data file), conduct a hypothesis test using Analysis of Variance to determine if there is a difference in the mean GPA for those who are unemployed vs. work part-time vs. work full-time. Report on your findings (100+ words, 3 or more sentences). In your report, be sure to include the results of the hypothesis test and indicate whether you are using a two-tail, upper-tail, or lower-tail test. Also include a chart comparing the means of the three groups. For this problem, a bar chart or column chart will work well; the display of the confidence intervals of the groups will also work.

Statistics: Hypothesis Testing

1. The mean construction time for a standard two-car garage by Arrowhead Construction Company is 3.5 days. The time for the construction process follows the normal distribution. The construction process is modified through the use of ‘precut and assembled roof trusses’ rather than onsite construction of roof rafters. This should shorten the construction time. A sample of 15 garages had a mean time of 3.40 days with a standard deviation of 0.8 days. Does use of the “precut and assembled roof trusses’ decrease the construction time? follow the hypothesis testing procedure using the 0.05 significance level by answering the following parts.

a) State the null and alternate hypotheses
b) State the decision rule
c) Compute the value of the test statistic
d) What is your decision regarding the null hypothesis?

2. The producer of a TV special expected about 40 percent of the viewing audience to watch a rerun of a 1965 Beatles concert. A sample of 200 homes revealed 60 to be watching the concert. At the 0.10 significance level. Does the evidence suggest that less than 40 percent were watching? Use the usual Hypothesis testing format.

a. state the null and alternate hypotheses
b. state the decision rule
c. compute the value of the test statistic
d. what is your decision regarding the null hypotheses

3A. A survey of 4000 college graduate determines that the mean length of time to earn a bachelor’s degree is 5.08 years and the standard deviation is 1.89 years. Construct a 96 percent confidence interval for the mean time required for all graduates to earn a bachelor’s degree.

B) A manufacturer of diamond drill bits for industrial production drilling and machining wishes to investigate the length of time a drill bit will last while drilling carbon steel. The production of the drill bits is very expensive, thus the number available for testing is small. A sample of 8 drill bits had a mean drilling time of 2.25 hours with a standard deviation of 0.5 hours. Construct a 95 percent confidence interval for the population mean. Is it reasonable for the manufacturer to claim that the drill bits will last 2.5 hours?

4. It was found that the mean length of 100 parts produced by a lathe was 20.05 mm with a standard deviation of 0.02mm.

Find the probability that a part selected at random would have a length
a) between 20.03 mm and 20.08 mm
b) between 20.06 mm and 20.07 mm
c) less than 20.01 mm
d) greater that 20.09 mm

5. The NPC, Inc. is a large mail order company that ships men’s shirts all over the United States and Canada. They ship a large number of packages from their warehouse in Delta, Ohio. Their goal is to have 95 percent of the shipments delivered in 4 days. For many years they have used Brown Tuck Inc., but recently there have been complaints about slow and inconsistent delivery. A sample of 10 recent shipments handled by Brown Truck showed a standard deviation in delivery time of 1.25 days. A sample of 16 shipments by Rapid Package Service showed a standard deviation in their delivery time of 0.45 days. At the 0.05 significance level is there more variation in the Brown Truck delivery time?

Answer the following questions.
a)-State the null and alternate hypotheses
b)-State the decision rule
c)-Compute the value of the test statistic
d)-What is your decision regarding the null hypothesis? Interpret the result

Statistics: Hypothesis testing

Please show all work:

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.

The test statistic is:
a)1.96
b) 2.00
c) 1.645
d) 0.05

The p-value is between:
a) .005 to .01
b) .01 to .025
c) .025 to .05
d) .05 to .10

At 95% confidence level, it can be concluded that the mean age is:
a) Not significantly different from 24
b) Significantly different from 24
c) Significantly less than 24
d) Significantly more than 24

Statistics: Hypothesis testing

See attached file.

Hypothesis Testing

Examine the given statement, then express the null hypothesis H0 and alternative hypothesis H1 in symbolic form. Be sure to use the correct symbol &#57502;(&#956; , p ,&#57544;&#963;)&#57503; for the indicated parameter.

1. The majority of college students own a vehicle.

2. The standard deviation of daily rainfall amounts in San Francisco is 0.66 cm.

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).

3. The test statistic in a right-tailed test is z = 2.50

4. The test statistic in a two-tailed test is z = – 0.55

Correlation
CPI 30.2 48.3 112.3 162.2 191.9 197.8
Cost of Pizza 0.15 0.35 1 1.35 1.5 2

1. Find the value of the correlation coefficient, r.

2. Find the critical value of r from Table A-6 using &#57527;=0.05 .

3. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables.

Statistics-Hypothesis Testing

Heather Carielli is a former student who earned a master degree at the University of Arkansas. When she randomly selected 16 new text books in the college book store she found that they had prices with a mean of $70.41 and a standard deviation of $19.70. Is there sufficient evidence to warrant rejection of a claim in the college catalog that the mean price of the textbook at the college is less than $75.00? use .05 significance level. Accept or the reject the null?