Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 8.100ACB
Durability of shock absorbers. A manufacturer of automobile shock absorbers was interested in comparing the durability of its shocks with that of the shocks produced by its biggest competitor. To make the comparison, one of the manufacturer’s and one of the competitor’s shocks were randomly selected and installed on the rear wheels of each of six cars. After the cars had been driven 20,000 miles, the strength of each test shock was measured, coded, and recorded. Results of the examination are shown in the table.
| Car Number | Manufacturer’s Shock | Competitor’s Shock |
| 1 | 8.8 | 8.4 |
| 2 | 10.5 | 10.1 |
| 3 | 12.5 | 12.0 |
| 4 | 9.7 | 9 3 |
| 5 | 9.6 | 9.0 |
| 6 | 13.2 | 13.0 |
- a. Explain why the data are collected as matched pairs.
- b. Do the data present sufficient evidence to conclude that there is a difference in the
mean strength of the two types of shocks after 20,000 miles of use? Use α= .05. - c. Find the approximate observed significance level for the test and interpret its value.
- d. What assumptions are necessary to apply a paired difference analysis to the data?
- e. Construct a 95% confidence interval for μd. Interpret the confidence interval.
- f. Suppose the data are based on independent random samples. Construct a 95% confidence interval for (μ1 – μ2). Interpret your result.
- g. Compare the confidence intervals you obtained in parts e and f. Which is wider? To what do you attribute the difference in width? Assuming in each case that the appropriate assumptions are satisfied, which interval provides you with more information about (μ1 – μ2)? Explain.
- h. Are the results of an unpaired analysis valid if the data come from a paired experiment?
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Students have asked these similar questions
A manufacturer of automobile shock absorbers was interested in comparing the durability of
its shock absorbers with that of the shock absorbers produced by its biggest competitor. To
make the comparison, one of the manufacturer's and one of the competitor's shock absorbers
were randomly selected and installed on the rear wheels of each of six cars. After the cars had
been driven 20,000 kilometres, the strength of each test shock absorbers was measured, coded
and recorded. It is given that the population variances are equal for both groups. The results of
the examination are shown in the Table below.
Manufacturer's shock absorbers
Car number
1
8.8
Competitor's shock absorbers
8.4
10.1
2
10.5
3
12.5
12.0
4
9.7
9.3
5
9.6
9.0
6
13.2
13.0
Determine whether there is sufficient evidence to conclude that there is a difference in the mean
strength of the two types of shock absorbers after 20,000 kilometres of use by using a level of
significance of 0.05.
A 2009 study shpwed that handling money reduces the perception of pain. Two groups of participants were asked to participate in a manual dexterity study. Half of the participants were given a stack of blank pieces of paper to count and the other half were given money to count. After the counting task, the participants were asked to dip their hands in 122 degree Farenheit water and rate how uncomfortable it was . The following data shows ratings of pain similar to the results obtained in the study.
Counting Money
Counting Paper
7
9
8
11
10
13
6
10
8
11
5
9
7
15
12
14
5
10
A. based on the sample data, does the treatment, does the treatment have a significant effect? Test with a=.01. ( make sure you have ALL the steps involved in a hypothesis test).
B. Calculate Cohens d to estimate the effect size.
C. What a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear on a research report.
Detergent manufacturers frequently make claims about effectiveness of their product. A consumer-protection service decided to test the five best selling brands of detergent in three water temperatures on their claim of producing the “whitest whites”. One hundred and fifty white sheets were equally soiled. Thirty sheets were washed in each of the five brands; 10 in cold water, 10 in warm water and 10 in hot water. After washing, the “whiteness” was measured with laser equipment.
Perform the appropriate post-hoc analyses and clearly state your conclusions about the performance of the different brands in lukewarm water.
Temperature
Dtrgent1
Dtrgent2
Dtrgent3
Dtrgent4
Dtrgent5
Cold
66
83
70
44
84
Cold
87
62
75
59
67
Cold
55
61
62
47
99
Cold
41
85
68
60
85
Cold
68
75
72
79
73
Cold
49
78
92
62
74
Cold
52
68
70
73
76
Cold
57
66
71
64
82
Cold
66
93
74
69
79
Cold
62
81
80
81
79
Lukewarm
78
63
71
70
87
Lukewarm
65
47
88
80
100
Lukewarm
68
88
90
78
83
Lukewarm…
Chapter 8 Solutions
Statistics for Business and Economics (13th Edition)
Ch. 8.2 - The purpose of this exercise is to compare the...Ch. 8.2 - Prob. 8.2LMCh. 8.2 - In order to compare the means of two populations,...Ch. 8.2 - Prob. 8.4LMCh. 8.2 - Prob. 8.5LMCh. 8.2 - Prob. 8.6LMCh. 8.2 - Independent random samples from normal populations...Ch. 8.2 - Two independent random samples nave been...Ch. 8.2 - Independent random samples of n1 = 233 and n2 =...Ch. 8.2 - Independent random samples from approximately...
Ch. 8.2 - Independent random samples selected from two...Ch. 8.2 - Lobster trap placement. Refer to the Bulletin of...Ch. 8.2 - Last name and acquisition timing. The speed with...Ch. 8.2 - Shared leadership in airplane crews. Human Factors...Ch. 8.2 - Performance-based logistics. Refer to the Journal...Ch. 8.2 - Drug content assessment. Refer to Exercise 4.123...Ch. 8.2 - Buy-side vs. sell-side analysts earnings...Ch. 8.2 - Homework assistance for accounting students. How...Ch. 8.2 - Comparing taste-test rating protocols....Ch. 8.2 - Producer willingness to supply biomass. The...Ch. 8.2 - Does rudeness really matter in the workplace?...Ch. 8.2 - Prob. 8.22ACICh. 8.2 - Is honey a cough remedy? Refer to the Archives of...Ch. 8.2 - Gender diversity of board of directors. The gender...Ch. 8.2 - Prob. 8.25ACACh. 8.3 - A paired difference experiment produced the...Ch. 8.3 - A paired difference experiment yielded nd pairs of...Ch. 8.3 - The data for a random sample of six paired...Ch. 8.3 - The data for a random sample of 10 paired...Ch. 8.3 - A paired difference experiment yielded the...Ch. 8.3 - Summer weight-loss camp. Camp Jump Start is an...Ch. 8.3 - Performance ratings of government agencies. The...Ch. 8.3 - Twinned drill holes. A traditional method of...Ch. 8.3 - Prob. 8.34ACBCh. 8.3 - I am not selling anything surveys. To improve...Ch. 8.3 - Consumers attitudes toward advertising. The two...Ch. 8.3 - Taking power naps during work breaks. Lack of...Ch. 8.3 - Acidity of mouthwash. Acid has been found to be a...Ch. 8.3 - Solar energy generation along highways. The...Ch. 8.3 - Impact of red light cameras on car crashes. To...Ch. 8.3 - Prob. 8.41ACICh. 8.3 - Alcoholic fermentation in wines. Determining...Ch. 8.4 - Consider making an inference about p1 p2, where...Ch. 8.4 - For each of the following values of , find the...Ch. 8.4 - Prob. 8.45LMCh. 8.4 - Prob. 8.46LMCh. 8.4 - Prob. 8.47LMCh. 8.4 - Prob. 8.48LMCh. 8.4 - The winners curse in auction bidding. In auction...Ch. 8.4 - Prob. 8.50ACBCh. 8.4 - Prob. 8.51ACBCh. 8.4 - Web survey response rates. Response rates to Web...Ch. 8.4 - Hospital administration of malaria patients. One...Ch. 8.4 - Traffic sign maintenance. The Federal Highway...Ch. 8.4 - Salmonella in produce. Salmonella infection is the...Ch. 8.4 - Angioplastys benefits challenged. More than 1...Ch. 8.4 - Entrepreneurial careers of MBA alumni. Are African...Ch. 8.4 - Predicting software defects. Refer to the PROMISE...Ch. 8.4 - Prob. 8.59ACICh. 8.4 - Religious symbolism in TV commercials. Gonzaga...Ch. 8.5 - Assuming that n1 = n2, find the sample sizes...Ch. 8.5 - Find the appropriate values of n1 and n2 (assume...Ch. 8.5 - Suppose you want to estimate the difference...Ch. 8.5 - Enough money has been budgeted to collect...Ch. 8.5 - Last name and acquisition timing. Refer to the...Ch. 8.5 - Homework assistance for accounting students. Refer...Ch. 8.5 - Vulnerability of relying party Web sites. Refer to...Ch. 8.5 - Conducting a political poll. A pollster wants to...Ch. 8.5 - Shared leadership in airplane crews. Refer to the...Ch. 8.5 - Solar energy generation along highways. Refer to...Ch. 8.5 - Angioplastys benefits challenged. Refer to the...Ch. 8.5 - Traffic sign maintenance. Refer to the Journal of...Ch. 8.6 - Use Tables V, VI, VII, and VIII in Appendix D to...Ch. 8.6 - Given v1 and v2, find the following probabilities:...Ch. 8.6 - For each of the following cases, identify the...Ch. 8.6 - For each of the following cases, identify the...Ch. 8.6 - Specify the appropriate rejection region for...Ch. 8.6 - Independent random samples were selected from each...Ch. 8.6 - Independent random samples were selected from each...Ch. 8.6 - Lobster trap placement. Refer to the Bulletin of...Ch. 8.6 - Prob. 8.81ACBCh. 8.6 - Mental health of workers and the unemployed. A...Ch. 8.6 - Drug content assessment Refer to Exercise 8.16 (p....Ch. 8.6 - Last name and acquisition timing. Refer to the...Ch. 8.6 - Prob. 8.85ACICh. 8.6 - Oil content of fried sweet potato chips. Refer to...Ch. 8.6 - Shopping vehicle and judgment. Refer to the...Ch. 8.6 - Is honey a cough remedy? Refer to the Archives of...Ch. 8 - List the assumptions necessary for each of the...Ch. 8 - Two independent random samples were selected from...Ch. 8 - Independent random samples were selected from two...Ch. 8 - Independent random samples were selected from two...Ch. 8 - Two independent random samples are taken from two...Ch. 8 - A random sample of five pairs of observations were...Ch. 8 - Prob. 8.95ACBCh. 8 - Prob. 8.96ACBCh. 8 - Prob. 8.97ACBCh. 8 - Hull failures of oil tankers. Refer to the Marine...Ch. 8 - Effectiveness of teaching software. The U.S....Ch. 8 - Durability of shock absorbers. A manufacturer of...Ch. 8 - NHTSA new car crash tests. Refer to the National...Ch. 8 - Diamonds sold at retail. Refer to the data for 308...Ch. 8 - Childrens recall of TV ads. A study examined...Ch. 8 - Is steak your favorite barbeque food? July is...Ch. 8 - Planning habits survey. American Demographics...Ch. 8 - Turnover rates in the United States and Japan....Ch. 8 - Smartphone usage differs by gender. The role of...Ch. 8 - Life expectancies of working women and housewives....Ch. 8 - Comparing purchasers and nonpurchasers of...Ch. 8 - Prob. 8.110ACICh. 8 - Racial profiling by the LAPD. Racial profiling is...Ch. 8 - State SAT scores. Refer to Exercise 2.27 (p. 60)...Ch. 8 - Rat damage to sugarcane fields. Poisons are used...Ch. 8 - Environmental impact study. Some power plants are...Ch. 8 - Instrument precision. When new instruments are...Ch. 8 - Cooling method for gas turbines. Refer to the...Ch. 8 - Average housing space per person. Even though...Ch. 8 - Positive spillover effects from self-managed work...Ch. 8 - Impact of gender on advertising. How does gender...Ch. 8 - Salaries of postgraduates. Refer to the Economics...Ch. 8 - Gambling in public high schools. With the rapid...Ch. 8 - CareerBank.com annual salary survey....Ch. 8 - Facility layout study. Facility layout and...
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