1. We ask if the attitudes toward fuel cost of 100 owners are hybrid electric cars (X=76) are different from those on a national survey of owners of non-hybrid cars (µ=65, s=24). Higher scores indicate a more positive attitude.
A) Is this a one or two tailed test?
B) In words what is the H0 and Ha?
C) Perform the z-test.
D) What do you conclude about the attitudes here?
E) Report your results in the correct format.
2. We measure the self esteem scores of a sample of statistics students, reasoning that this course may lower their self esteem relative to that of the typical college student (µ=55 and s=11.35) We obtain these scores:
44 55 39 17 27 38 36 24 36
A) Summarize your sample data.
B) Is this a one tailed or two tailed test? Why?
C) What are the H0 and Ha?
D) Compute z-statistic
E) With alpha =0 .05 what is z-critical?
F) What should we conclude about the relationship here?
Perform a 5 step hypothesis test on the given data for the following null and alternative hypothesis:
Null Hypothesis – TB is greater in the U.S. than foreign countries between 1993-2009
Alternative Hypothesis – TB is less in the U.S. than in foreign countries between 1993-2009.
See the attached files.
MEALS-ON-TRACKS
Contract specifications require (among other things) that Meals-On-Tracks, Inc., deliver 14,400 combat meals with a mean weight of 8.5 ounces. You have been given a technical report with the results of a sample of 25 dry combat meals taken from today’s shipment. The sample had a mean weight of 8.0 ounces and a standard deviation of .1 ounce.
The contractor contends that the difference between the specified weight and the sample weight is due to sampling error.
A. Is it likely that the contractor is right?
B. That is, would you accept the shipment?
Fill in the following table
use a 5 percent significance level for all statistical analysis.
_
Statistic X s n a
Value
Please review the attached problem and help.
A department store manager claims that at least 45% of persons who visited this store make a purchase. In a sample of 400 persons who visited the store 150 made a purchase. Test the manager’s claim at the 3% significance level.
a. State the null and alternate hypothesis.
b. Determine the rejection region for the decision rule.
c. Which equation listed below would you use?
d. Using the statistical calculator or manual calculation what is the observed statistic and what is your decision regarding the null hypothesis? Provide a one sentence answer.
Problem:
Past records suggest that the mean annual income, mu1, of teachers in state of pennsylvania is less than or equal to the mean annual income, mu2, of teachers in Illinois. In a current study, a random sample of 15 teachers from pennsylvania and an independent random sample of 15 teachers from Illinois have been asked to report their mean annual income. The data obtained are as follows:
Annual income in dollars:
Pennsylvania: 48328, 50306, 60240, 51475, 45907, 53775, 41891, 54579, 56691, 49082, 50803, 54491, 46189, 45232, 41828
Illinois: 43658, 52307, 39589, 45643, 44440, 39322, 32237, 50639, 39983, 37811, 36605, 44425, 40391, 56138, 48695
The population standard deviation for mean annual income of teachers in Pennsylvania and in Illinois are estimated as 6400 and 6100, respectively. It is also known that both populations are approximately normally distributed. At the 0.01 level of significance, is there sufficient evidence to reject the claim that the mean annual income of teachers in state of Pennsylvania is less than or equal to the mean annual income of teachers in Illinois? Perform a one-tailed test.
Question:
H0:_____
H1:_____
Type of test statistic: (Z, t, F, or Chi squared)
Value of test statistic:______
The p-value:_______
Can we reject the claim that the mean annual income of teachers from Pennsylvania is less than or equal to the mean annual income of teachers from Illinois?
The manufacturer of a compact disc player wanted to know whether a 10 percent reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the disc player at the reduced price. At seven randomly selected outlets, the disc player was sold at the regular price. Reported below is the number of units sold last month at the sampled outlets. At the 0.01 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales?
Regular price 138 121 88 115 141 125 95
Reduced Price 128 134 152 135 114 106 112 120
A medical board approved the average stay in the hospital for patients that have a particular operation as 6.0 days. However, the insurance company the claims that the average hospital stay for patients has been substantially longer than 6.0 days. To examine this claim a sample of 100 patients who had this operation in the last year is selected. Perform a test of hypothesis to determine what decision should be made if the sample mean for the 100 patients is 6.32 days and the standard deviation is 0.64 days. Test your hypothesis at α = 0.05 level of significance.
In the news recently a New Jersey representative wants to introduce a bill banning smoking while driving to save lives.
What study would you design to support his case?
What is the null hypothesis? Alternative hypothesis? How would you sample? How many would you include in your sample? What level of significance would you choose?
Ten automobiles were driven on a measured test track – once with standard gasoline with no additive and once with an additive supposed to increase miles per gallon (mpg). The results are given below:
mpg / car # 1 2 3 4 5 6 7 8 9 10
without additive 19 22 25 18 26 21 23 28 24 24
with additive 22 24 26 21 27 24 26 32 23 27
Test the null hypothesis that the additive has no or negative effect against the alternative hypothesis that it has a positive effect on mileage at the alpha = 0.05 level of significance.
My initial thoughts are:
Ho: mean(w/o additive) >= mean (w /additive)
Ha: mean(w/o additive) < mean (w/additive)
So this appears to be a one-tailed t-statistic with 2 population means, is this right? How would this problem work? Formulas appreciated.
For the attached spreadsheet assume equal variances for the two populations.
A) Test the null hypothesis that the average length of service for males is the same as for females.
B) Test the null hypothesis that the average length of service for individuals without prior call center experience is the same as those with experience.
C) Test the null hypothesis that the average length of service for individuals with a college degree is the same as for individuals without a college degree.
D) Now conduct tests of hypothesis for equality of variances. Were your assumptions of equal variances valid? If not, repeat the test(s) for means using the unequal variance test.
Stonehenge’s main ditch was dug in a series of segments. Excavations at the base of the ditch uncovered a number of antlers which bore signs of heavy use. These antlers could have been used by the builders as picks or rakes. The fact that no primary silt was discovered beneath the antlers suggests that they were buried in the ditch shortly after its completion. Another researcher, Phillip Corbin, using an archeological markings approach, had previously claimed that the mean date for the construction of the ditch was 2950 BC. A sample of nine age estimates from unshed antlers excavated from the ditch produced a mean of 3033.1 BC, with standard deviation 66.9 years. Assume that the ages are normally distributed with no obvious outliers. At a significance level, alpha = 0.05 significance level, is there any reason to dispute Corbin’s claim?
The production line that packages boxes of raisins at a snack food manufacturer will be considered operating properly if the average weight of the boxes of raisins is 1.5 ounces with a standard deviation of 0.1 ounces. A random sample of 16 boxes showed an average weight of 1.45 ounces.
1. How can I find the null and alternative hypothesis to determine if the production line is operating properly.
2. What additional assumption is needed before we can perform a test to determine whether the production line is operating properly?
3. State the value of the correct rejection region for α = 0.05
4. State the correct rejection region for α = 0.01
5. 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?
————————————————————————–
An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments based upon the size of the apartment as defined by square footage. A sample of 25 apartments in a particular residential neighborhood was selected and the information gathered revealed the following:
Apartment Rent ($) Size (sf) Apartment Rent ($) Size (sf)
1 950 850 14 1,800 1369
2 1,600 1450 15 1,400 1175
3 1,200 1085 16 1,450 1225
4 1,500 1232 17 1,100 1245
5 950 718 18 1,700 1259
6 1,700 1485 19 1,200 1150
7 1,650 1136 20 1,150 896
8 935 726 21 1,600 1361
9 875 700 22 1,650 1040
10 1,150 956 23 1,200 755
11 1,400 1100 24 800 1000
12 1,650 1285 25 1,750 1200
13 2,300 1985
1. Use the least squares method to find the regression coefficients b0 and b1.
2. State the simple linear regression equation
3. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet with a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. What would you recommend to them? Why?
Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, they use different media to reach potential buyers. The mean annual family income for 75 people making inquires at the first development is $150,000, with a standard deviation of $40,000. A corresponding sample of 120 people at the second development had a mean of $180,000, with a standard deviation of $30,000. At the .05 significance level, can Fairfield conclude that the population means are different?
Ms. Lisa Monnin is the budget director the New process Company. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample
Sales $ 131 135 146 165 136 142
Audit 130 102 129 143 149 120 139
At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?
The management of Discount Furniture, a chain of discount furniture stores in the Northeast dwsigned an incentive plan for sales people. To evaluate this innovative plan, 12 salespeople were selected at random and their weekly incomes before and after the plan were recorded.
Salesperson Before After
Malone $320 $340
Quick 290 285
Jackson 421 475
Jones 510 510
Sloan 210 210
Walker 402 500
Mancuso 625 631
Loma 560 560
Cuso 360 365
Utz 431 431
Kushner 506 525
Lawton 505 619
Was there a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.
A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation in the population?
Lester Hollar is Vice President for Human Resources for a large manufacturing company. In the recent years hr has noticed an increase in absenteeism that he thinks is related to general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of das each was absent in the six months before the exercise program began and in the last six months. Below are the results. At the 0.05 significance level, can he conclude the number of absences has declined? Estimate the p-value.
Your director has banned the use of all artificial fingernails, claiming their use contributes to patient infections in the unit. After multiple discussions the director has allowed you to do a research study to determine if the use of artificial fingernails causes increases in infection rates. You would really like to prove that their use does not contribute to infection rates. Without worrying about the research design in this case, or even how you might research it, state
1. The null and alternate that you might use.
2. What alpha you might use and why
3. What rejecting the null would mean
4. What failing to reject the null would mean
5. What a type I error is in this case and the consequences of it?
6. What a type II error is in this case and the consequences
7. Which error is more important in this case.
A leasing firm claims that the mean number of miles driven annually, u, in its leased cars is less than 13,340 miles. A random sample of 13,239 cars leased from this firm had a mean of annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1680 miles. Assume that the population is normally distributed. Is there support for the firm’s claim at the 0.1 level of significance?
Listed below is the rate of return for one year (reported in percent) for a sample of 12 mutual funds that are classified as taxable money market funds.
4.63 4.15 4.76 4.70 4.65 4.52 4.70 5.06 4.42 4.51 4.24 4.52
Using the .05 significance level is it reasonable to conclude that the mean rate of return is more than 4.50 percent?
1. A maker of golf balls has developed a new ball technology and is interested in estimating the mean difference in driving distance for this new ball versus its existing best-seller. To conduct the test the developers selected six professional golfers and had each golfer hit each ball one time. The distances travelled were:
Golfer Distance with existing ball distance with new ball
1 278 285
2 299 301
3 280 276
4 295 300
5 268 276
6 305 315
Given that distances are normally distributed, test the hypothesis that there is no difference in distance travelled by both types of golf balls. Note that the same golfer hit each of the two balls, so the distance a ball travels depends to some extent upon the individual hitting the ball.This violates the requirement of independence necessary for all of the two-sample tests. In the two-sample cases the data from each population must be drawn independently and randomly from that population. With a paired model the differences between the populations must be independent of each other.
2. A random sample of ten advertisements taken from news magazines had the following reading difficulty levels:
9.7 5.6 6.0 5.5 8.2 6.1 4.8 6.5 6.0 6.7
A second random sample of 12 advertisements taken from financial magazines had the following reading difficulty levels:
9.4 7.6 6.9 7.2 7.5 8.0 6.9 6.6 7.5 7.8 6.8 6.0
Test, at a .05 level of significance, the hypothesis that advertisements published in news magazines had greater variation in reading difficulty levels than those published in financial magazines.
3. A random of 8 female high school Juniors and a random sample of 8 male high school. Juniors at a particular school took the SAT and made the following scores:
Student Female SAT Scores Male Sat Scores
1 640 530
2 590 550
3 590 580
4 640 620
5 590 490
6 585 500
7 575 550
8 550 500
Test, at a .05 level of significance, the hypothesis that female Juniors at this school score 25 points higher on the SAT than do males, given SAT scores are normally distributed.
4. A think tank research team was studying the relationship between idea generation by groups with and without a moderator. For a random sample of 40 groups with a moderator the mean number of ideas generated per group was 78.0 with a standard deviation of 24.4. For a random sample of 30 groups without a moderator the mean number of ideas generated was 63.5 with a standard deviation of 20.2. Test, at a .05 level of significance, the hypothesis that groups with a moderator generate over 10 more ideas than groups without a moderator.
5. The United Way raises money for community charity activities. In one particular community the fund raising committee was concerned about whether there is a difference in the average contribution of private-sector employees and government employees. Random samples of people who had been contacted about contributing last year were selected. It was found that of the 50 private-sector employees the average contribution was $309.45 with a standard deviation of $67.75. For the 60 government employees the average contribution was $230.25 with a standard deviation of $51.52. Given that charitable contribution amounts are known to be normally distributed, can we be 95% confident that private sector employees contribute $100 more on average than government employees?
6. Datatrac reported that a random sample of 30 credit unions charged an average interest rate of 12.15% with a standard deviation of 2.86% on credit cards they had issued, while a random sample of 40 banks charged an average of 15.08% interest with a standard deviation of 1.90 % on credit cards they had issued. Test, at a .01 level of significance, the hypothesis that credit unions charge less interest on their credit cards than do banks.
7. A random sample of 337 homeowners in Los Angeles County contained 133 who had purchased earthquake insurance, while a random sample of 521 homeowner in Contra Costa county in California contained 117 who had purchased earthquake insurance. Los Angeles County is the closest of the two to a major earthquake fault. Do the sample results support the contention that closer proximity to major earthquake faults result in higher proportions of earthquake-insured residents?
8. The number of hours per week students claim to spend studying for introductory finance and accounting classes were obtained from a random sample of 12 finance students and another of 10 accounting students. The numbers reported were:
Finance 10 6 8 10 12 13 11 9 11 11 8 9
Accounting 13 17 14 12 16 19 15 16 11 5
Test, at a .05 level of significance, the hypothesis that finance students spend fewer hours studying that do accounting students, given normality.
You want to check the claim that the Laurelhurst area has higher day care charges then the non Laurelhurst areas. Test the hypothesis that the Laurelhurst area has a higher daycare charge per month from the date below.
LAURELHURST NON-LAURELHURST
500 500
625 625
440 500
550 350
600 300
500 550
475
325
350.
Refer to the Baseball 2005 data set(just 46) at, which report information on the 30 major League baseball teams for the 2005 season. (See attachment).
Can also be found at:
http://highered.mcgraw-hill.com/sites/0073030228/student_view0/index.html
a. Conduct a test of hypothesis to determine whether the mean salary of the teams was different from 80.0 million. Use the .05 significance level.
b. Conduct a test of hypothesis to determine whether the mean attendance was more than 2, 000, 000 per team.
An Ice Cream manufacturer wants to know if their claim of 64 oz. per each half gallon container is any less than 64 oz.
1) How would you set up the hypotheses? One or Two tailed test? If one tailed, upper or lower?
2) With 30 samples, alpha at 0.05, a standard deviation at 0.3, and a mean of 63.98, perform the z-test.
3) What is the outcome of their claim?
A legal researcher is studying the age distribution of juries by comparing them with the overall age distribution of available jurors. The researcher claims that the jury distribution is different from the overall distribution; that is, there is a noticeable age bias in jury selection in this area.The table shows the number of jurors at a county court in one year and the percent of persons
residing in that county, by age. Use the population distribution to find the expected juror frequencies.Test the researcher’s claim at a = 0.01.
21-29 30-39 40-49 50-59 60 and above
Jury 45 128 244 359 359
Population 20.5% 21.7% 18.1% 17.3% 22.4%
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
1. State the hypothesis.
2. State the decision rule.
3. Calculate the test statistic.
4. What is your decision regarding the Null Hypothesis H0?
Please use Excel—–In addition, to showing printouts, state the results of the hypothesis test in terms of the question using complete sentences and examples( I did the other 3?but was’nt so sure about these).
1. The Mac burgher restaurant chain claims that the mean waiting time of customers for service is 3 minutes and a population standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road Mac burger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we say that the mean waiting time is less than 3 minutes?
2. A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A random sample of 50 people who joined the new Weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? Determine the p-value.
3. According to a recent survey Americans get a mean of seven hours sleep per night. A random sample of 50 students at West Virginia University revealed that the mean numbers of hours slept last night was 6 hours and 48 minutes (6.8 hours). The Standard deviation of the sample was 0.9 hours. Is it reasonable to conclude that the students at West Virginia sleep less than the typical American?
4. According to the Coffee Research Organization (http://www.coffeeresearch.org) the typical American coffee drinker consumes an average of 3.1 cups per day. A sample of 12 senior citizens revealed they consumed the foll. Amounts, reported in cups of coffee yesterday.
3.1 3.3 3.5 2.6 2.6 4.3 4.4 3.8 3.1 4.1 3.1 3.2
At the .05 significance level, does the sample data suggest there is a difference between the national average and the sample information from senior citizens?
1. Given the following data from two independent samples from which the population standard deviation is known, conduct a two-tailed hypothesis test to determine if the first sample mean is smaller than the second sample mean, given a 0.01 level of significance.
n1 = 42 n2 = 30
xbar1= 39 xbar2 = 25
sigma1=8 sigma2 = 6
Conduct a two-tailed hypothesis test given the information below.
2. Assuming that the population standard deviations are unknown, but equal for male and female Grade Point Averages (GPAs), use the following sample data to test whether the averages are different at the 0.05 level of significance.
Male GPA’s Female GPA’s
Sample Size 12 13
Sample Mean 2.8 4.95
Sample Standard Deviation .25 .8
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?
The scores of 133 males and 162 females on a test that measures a person’s feelings are shown in the table below. Your conjecture is the “the feelings” of males and females in the population are different. Run a hypothesis test to check this proposition.
Group Sample size x-bar Standard Deviation of the sample
Male 133 25.34 5.05
Female 182 24.94 5.44
For a number of years… In the first year after the change, there were 56- survivors in a class of 800. Is this increase explainable as simply sampling variability? Test at a=0.01.
Please see attached.
Let X…Is the battery likely to last more than 5 years?
Please see attached.
Seven skulls… Use these statistics in a test of the hypothesis that these skulls belong to a race previously found nearby in which the average width if known to be 146mm. Assume a nearly normal population. Perform the test a=0.1.
Please see attached.
Please help me to understand how to perform the given testing method:
Perform the following hypothesis test using the 5 step hypothesis testing method:
Null Hypothesis, Ho: b = 0
Alternate Hypothesis, Ha: b # 0
Mean = 1.87
Standard Deviation = 0.63
Sample Size = 3
Significance Level, alpha = 0.05
Here are some things I need help with:
? ALWAYS write out the NULL & HYPO (they come as a set) even if
the assignment does not ask you to do so
? Even though you write hypotheses using mathematical notations,
it is important to also get in the habit of writing them in words too…
things do get more complicated
? Always state the decision rule:
o The NULL hypothesis is NOT rejected because (fill in the blank)
therefore there is no support for the HYPOTHESIS that (copy & paste your
hypothesis here)
o The NULL hypothesis is rejected because (fill in the blank)
therefore there is support for the HYPOTHESIS that (copy & paste your
hypothesis here)
? TAILS: this concept is a big deal. You can understand
?
MEAN TO A MANAGER??” It will be good practice for later assignments
Problem 9.23 The data on the file CONCRETE1.xls represent the compressive strength in thousands of pounds per square inch (psi) of 40 samples of concrete taken two and seven days after pouring. (NOTE: the data is on the CD and is named CONCRETE1.XLS…it is also in the table below)
Sample Two days Seven days Sample Two days Seven days
1 2.83 3.505 21 1.635 2.275
2 3.295 3.43 22 2.27 3.91
3 2.71 3.67 23 2.895 2.915
4 2.855 3.355 24 2.845 4.53
5 2.98 3.985 25 2.205 2.28
6 3.065 3.63 26 3.59 3.915
7 3.765 4.57 27 3.08 3.14
8 3.265 3.7 28 3.335 3.58
9 3.17 3.66 29 3.8 4.07
10 2.895 3.25 30 2.68 3.805
11 2.63 2.85 31 3.76 4.13
12 2.83 3.34 32 3.605 3.72
13 2.935 3.63 33 2.005 2.69
14 3.115 3.675 34 2.495 3.23
15 2.985 3.475 35 3.205 3.59
16 3.135 3.605 36 2.06 2.945
17 2.75 3.25 37 3.425 4.03
18 3.205 3.54 38 3.315 3.685
19 3 4.005 39 3.825 4.175
20 3.035 3.595 40 3.16 3.43
a. At the .01 level of significance, is there evidence that the average strength is less at two days than at seven days?
? ANSWER:
b. What assumption is necessary to perform this test?
? ANSWER:
c. Find the p-value and interpret its meaning.
? ANSWER:
Problem 9.25 A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?” Of the 240 males, 136 answered yes and of the 260 females, 224 answered yes.
a. Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing, at the .01 level of significance?
? ANSWER:
b. Find the p-value and interpret its meaning.
? ANSWER:
c. Set up a 99% confidence interval estimate of the difference between the proportion of males and females who enjoy shopping for clothing.
? ANSWER:
d. Compare the results of A & C.
? ANSWER:
e. What would be your answer to A-C if 206 males enjoyed shopping for clothing?
? ANSWER:
Problem 9.43 The director of training for a company manufacturing electronic equipment is interested in determining whether different training methods have an effect on the productivity of assembly-line employees. She randomly assigns 42 recently hired employees to two groups of 21. The first group receives a computer-assisted, individual-based training program, and the others receives a team-based training program. Upon completion of the training, the employees are evaluated on the time (in seconds) it takes to assemble a part. The results are as follows: (NOTE: the data is on the CD and is named TRAINING.XLS and below)
COMPUTER-ASSISTED, INDIVIDUAL-BASED TRAINING PROGRAM TEAM-BASED TRAINING PROGRAM
19.4 17.7 16.5 22.4 17.1 23.7
16.7 16.1 17.7 13.8 18 17.4
20.7 19.8 16.2 18.7 28.2 23.2
19.3 16.8 17.4 18 21.7 20.1
21.8 19.3 16.4 19.3 20.8 12.3
16.8 14.7 16.8 20.8 30.7 15.2
14.1 16 18.5 15.6 24.7 16
a. Using a .05 significance level, is there evidence of a difference between the variables in assembly times (in seconds) of employees trained in a computer-assisted, individual-based training program and those trained in a team-based program? HINT: we just studied a specific type of test.
? ANSWER:
b. On the basis of the results obtained in (a), is it appropriate to use the pooled-variance t test to compare the means of the two groups? Discuss.
? ANSWER:
Problem 9.53 The pet-drug market is growing very rapidly. Before new pet drugs can be introduced into the marketplace, they must be approved by the U.S. Food & Drug Administration (FD). In 1999, the Novartis company was trying to get Anafranil, a drug to reduce dog anxiety, approved. According to an article (Elyse Tanouye, “The Ow in Bowwow: With Growing Market in Pet Drugs, Makers Revamp Clinical Trials.” Wall Street Journal, April 13, 1999), Novartis had to find a way to translate a dog’s anxiety symptoms into numbers that could be used to prove to the FDA that that the drug had a statistically significant effect on the condition. (PHSTAT not needed for this problem)
a. What is meant by the phrase “statistically significant effect?”
? ANSWER:
b. Consider an experiment where dogs suffering from anxiety are divided into two groups. One group will be given Anafranil, and the other will be given a placebo (a drug without active ingredients). How can a dog’s anxiety symptoms be translated into numbers? In other words, does a continuous random variable (X1), the measurement of effectiveness of the drug Ananfranil, and X2, the measurement of effectiveness of the placebo.
? ANSWER:
c. Building on your answer to part (b), define the null & hypothesis for the study.
? ANSWER:
11. Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.
Treatment 1 Treatment 2 Treatment 3
8 3 3
11 2 4
10 1 5
3 4
2
1. State the null hypothesis and the alternate hypothesis.
2. What is the decision rule?
3. Compute SST, SSE, and SS total.
4. Complete an ANOVA table.
5. State your decision regarding the null hypothesis.
6. If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence.
The breaking strengths of cables have a mean of 1825 lbs and a standard deviation of 65 lbs. The company claims that there is an improvement in breaking strength. To evaluate this claim, 16 cables are randomly chosen and tested — their mean breaking strength is 1859 lbs. Can we support, at the 0.05 significance level, the claim that the mean breaking strength has increased?
Perform a one-tailed test. Then fill in the table below [see attachment].
There are six short responses required for this hypothesis test worksheet (please see the attached file).
The lives of many people are affected by a fear that prevents them from flying. The Marist Institute for Public Opinion conducted a poll of 1014 adults, 48%of whom were men. The results reported in USA Today showed that 12% of men and 33% of the women fear flying.
a) Is there sufficient evidence to conclude that there is a significant difference between the percentage of men and the percentage of women who fear flying?
b) Construct a 95% confidence interval for the percentage of men who fear flying.
c) Based on the results from (b) , which is typical of the statement that would be reported in a newspaper or magazine. “Based on the Public opinion poll, the percentage of men who feared flying is 12% with a margin of error of ?_____?
Using the data set below for the Hypothesis Testing Paper, a new hypothesis test (such as large sample size, small sample size, means and/or proportions, one-and two-tailed tests) that can perform on the data below I pulled together. Perform the five-step hypothesis test on the data and describe the results of the tests and compare the results to the results of the test peformed from my previous Hypothesis test.
If when you do a Hypothesis test about the Population Mean, somehow you have the actual value for the Population Standard Deviation. Suppose that you were able to get a sample of size 100, and did not know the Population Standard Deviation. What can you do to still carry out the Hypothesis test?
Suppose that a small college claims majority of their students graduate within four years. A random survey of 250 alumni finds that 145 of them graduated within 4 years.
Given that the pair of hypotheses that correspond to the claim are as follows:
H0: p <= 0.50
H1: p > 0.50
Find the critical values for the hypothesis test. Assume that the significance level is a=0.03.
Answer: z = ________________
Use the ratio or interval numerical data from one of the data sets available through the Data Sets link on your student website.
Develop one research question from which you will formulate a research hypothesis. ” Price of property is greater closer to the city”
Distance Vs Price
Prepare a 1,050- to 1,750-word paper describing the results of a hypothesis test of one population mean or population proportion.
Include the following in your paper:
o Formulate both a numerical and verbal hypothesis statement regarding your research issue.
o Perform the five-step hypothesis test on data pertaining to your selection.
o Describe the results of your test and explain how the findings from this hypothesis testing may be used to answer your research question.
o Include your raw data tables and the results of the computations of your z-test or t-test using graphical and tabular methods of displaying data and results.
o Format your paper consistent with APA guidelines.
Suppose that a company claims that 67% of their employees (about 2/3) buy annual parking permits for parking at their workplace. A random survey of 120 employees finds that 62 of them have annual parking permits.
Given that the pair of hypotheses that correspond to the claim are as follows:
H0: p = 0.67
H1: p # 0.67
Find the critical values for the hypothesis test. Assume that the significance level is a=0.01
Answer: z = ± ________________
Suppose that a small college claims that they graduate at least 500 students every semester. A random sample of 31 semesters yields a sample mean of 420 with a sample standard deviation of 65.
H0: m >= 500
Ha: m < 500
Find the critical value for the hypothesis test. Assume that the significance level is a=0.02.
Answer z=_________________________
Round your final answer to two decimal places.
A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 25 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounces. Use a 0.05 level of significance and test to see if the machine is in perfect adjustment (perform all six steps of hypothesis testing, including p-values).
The manager of Tammy Corporation wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned five employees to each of the three proposed work schedules. The following table shows the units of production (per week) under each of the work schedules.
Work Schedule (Treatments)
Schedule 1 Schedule 2 Schedule 3
50 60 70
60 65 75
70 66 55
40 54 40
45 57 55
At a 0.05 level of significance, determine if there is a significant difference in the mean weekly units of production for the three types of work schedules (perform all six steps of hypothesis testing and show the ANOVA table).
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.
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 alpha = 0.025?
Attachments.
Refer to the real estate data which reports information on homes sold in Denver Colorado last year.
a. A recent article in Denver post indicated that the mean selling price of the homes in the area is more than $220,000. can we conclude that the mean selling price in the Denver area is more than $220,000. Use the .01 significance level. What is the p-value?
d. Determine the proportion of homes that have a pool. At the .05 significance level, can we conclude that less than 40 percent of the homes in the Denver area had a pool? What is the p-value?
I like to know how to complete the problem by hand using formulas The data is is my previous post.
Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.
Sales ($) 131 135 146 165 136 142
Audit ($) 130 102 129 143 149 120 139
At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?
The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.
Salesperson Before After
Sid Mahone $320 $340
Carol Quick 290 285
Tom Jackson 421 475
Andy Jones 510 510
Jean Sloan 210 210
Jack Walker 402 500
Peg Mancuso 625 631
Anita Loma 560 560
John Cuso 360 365
Carl Utz 431 431
A. S. Kushner 506 525
Fern Lawton 505 619
Was there a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.
A data set can be found at the Data and Story Library site: http://lib.stat.cmu.edu/DASL by searching for Friday the 13th materials.
The data were collected in an effort to study various aspects of human behavior on Friday 13th by monitoring the change in traffic patterns between Friday the 6th and the subsequent Friday the 13th along with shopping traffic and accident reports.
A. Use the data in the accident category from the Friday the 13th data file, along with an appropriate hypothesis test to answer the question: Is Friday the 13th any more unlucky than Friday the 6th?
B. Do more people shop on Friday the 13th? Justify your answer by formulating and executing a hypothesis test.
Describe a 5-step hypothesis test utilizing the chi-squared “goodness of fit” technique) for a particular claim related to your work or life environment. You need to state the claim, define the null and alternate hypotheses, identify the test significance and the test statistic, and state the decision rule that will be used. The decision rule may be based on critical values or on the p-value approach. You do not need to collect data and actually conduct the test calculations unless you wish to do so
Three groups of students, 5 in each group, were receiving therapy for severe test anxiety. Group 1 received 5 hours of therapy, group 2 – 10 hours and group 3 – 15 hours. At the end of therapy each subject completed an evaluation of test anxiety (the dependent variable in the study). Did the amount of therapy have an effect on the level of test anxiety? Please develop the appropriate hypothesis test at a .05 level of significance and show and label all steps in your test. The three groups of students received the following scores on the Test Anxiety Index (TAI) at the end of treatment.
TAI Scores for Three Groups of Students
Group 1 – 5 hours Group 2 – 10 hours Group 3 – 15 hours
38 45 41
40 42 42
43 43 40
42 45 43
40 43 40
During 2002, college work – study students earned a mean of $1252. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $1277 during the year, with a standard deviation of $210. Would a one-tail test at the 0.05 level suggest the average earnings of this university’s work-study students were significantly higher than the national mean?
An office equipment company advertises that it will deliver equipment within 15 days of purchase. A sample of 49 past deliveries is taken to test whether company’s advertisement is valid. The delivery time for this sample was 16.2 days with a sample standard deviation of 5.6 days. Which of the following is correct
* What is the null?
* If test of hypothesis at 5% level of significance is desired, what is (are) the critical value(s) for test statistics?
1.96
-1.96
+1.96
1.645
-1.645
+1.645
None of the above answers is correct
*****************************************
* What is the test statistic value?
1.5
1.6
1.7
1.8
1.9
2.0
None of the above answers is correct
******************************************
* ASSUMING that null hypothesis can not be rejected, what statement can be made concerning validity of company advertisement?
The Rocky Mountain district sales manager of Rath Publishing, Inc., a college textbook publishing company, claims that the sales representatives make an average of 36 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 32 sales representatives reveals that the mean number of calls made last week was 37. The standard deviation of the sample is 2 calls. Using the 0.10 significance level, can we conclude that the mean number of calls per salesperson per week is more than 36?
H0 : m <= 36
H1 : m > 36
A United Nations report shows the mean family income for Mexican migrants to the United States is $27,150 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 30 Mexican family units reveals a mean to be $29,500 with a sample standard deviation of $11,150. Does this information disagree with the United Nations report? Apply the 0.01 significance level.
(a) State the null hypothesis and the alternate hypothesis.
(b) State the decision rule for 0.01 significance level. (Round your answers to 3 decimal places.)
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
(d) Does this information disagree with the United Nations report? Apply the 0.01 significance level.
Here are heart rates for a sample of 30 students before and after a class break. At alpha = .05, was
there a significant difference in the mean heart rate? (a) State the hypotheses. (b) State the decision
rule and sketch it. (c) Find the test statistic. (d) Make a decision. (e) Estimate the p-value and
interpret it.
Heart Rate Before and After Class Break:
Student Before After Student Before After
1 60 62 16 70 64
2 70 76 17 69 66
3 77 78 18 64 69
4 80 83 19 70 73
5 82 82 20 59 58
6 82 83 21 62 65
7 41 66 22 66 68
8 65 63 23 81 77
9 58 60 24 56 57
10 50 54 25 64 62
11 82 93 26 78 79
12 56 55 27 75 74
13 71 67 28 66 67
14 67 68 29 59 63
15 66 75 30 98 82
The Gibbs Baby Food Company wishes 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 of 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, with a standard deviation of 2.9 pounds. At the .05 significance level, can we conclude that babies using the Gibbs brand gained less weight? Compute the p-value and interpret it.
Please see sample problem in attachment.
—
Consider the following hypothesis test
H0: mu1 – mu2 = 0
Ha: mu1 – mu2 =/ 0
The following results are for two independent samples taken from the two populations.
Sample 1 Sample 2
n1 = 80 n2 = 70
mu1 = 104 mu2 = 106
s1 = 8.4 s2 = 7.6
1. What is the value of the test statistic?
2. With alpha = .05, what is your hypothesis testing conclusion?
**Both the null hypothesis and the alternative hypothesis need to be stated**
—
I need to have the work shown (IE formulas used, etc) so I can learn how to solve this type of problem through step by step solving process.
Thanks
From her firm’s computer telephone log, an executive found that the mean length of 64 telephone calls during July was 4.48 minutes with a standard deviation of 5.87 minutes. She vowed to make an effort to reduce the length of calls. The August phone log showed 48 telephone calls whose mean was 2.396 minutes with a standard deviation of 2.018 minutes.
(a) State the hypotheses for a right-tailed test.
(b) Obtain a test statistic and p-value assuming unequal variances. Interpret these results using α = .01.
(c) Why might the sample data not follow a normal, bell-shaped curve? If not, how might this affect your conclusions?
The duration of human gestation is on average 40.5 weeks. In a maternity ward, we note the gestational age of 100 consecutive newborns. The sum of these ages is equal to 3850 weeks and the standard deviation is 5 weeks. We believe that it is a ward for premature births. Do we have enough evidence to support our claim? Make sure you specify the test statistic that you are using and properly formulate Ho (Null Hypothesis) and Ha (Alternate Hypothesis).
The “Washington State Population Survey” is conducted biennially to support research on health care issues and other economic factors affecting Washington State residents. Data from the survey is publicly available and is used extensively in research by many organizations. See link for description of survey if you wish:
http://www.ofm.wa.gov/sps/2004/default.asp
The 2004 survey asks the question, “What kind of business or industry is your main job in?” Two of the more than 24 choices available are;
1) Health Care and Social Assistance
2) Finance and Insurance
The survey also collects data regarding hourly wage, gender, age, and many other socio-economic and demographic variables. If you were planning your career future in this state you might find this data useful in making a decision regarding which of the two industries provides a better financial outlook.
In the attached file, the data presented represents independent samples of two populations, measuring the hourly wage earned by those employed in the two industries. Some descriptive statistics are also calculated for you. At the 5% level of significance, can you state that there is a significant difference in mean hourly wage between the two industries?
I have worked on this for several hours but I can’t seem to get a full understanding of the hypothesis testing process. Can you please
use the 5-step hypothesis testing process and include all the details of any calculations you make or explanation of how you arrive at any values you determine? Thanks!
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