Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
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?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
4.96 The breaking strengths for 1-foot-square samples of a particular synthetic fabric are approximately normally distributed with a mean of 2,250 pounds per square inch (psi) and a standard deviation of 10.2 psi. Find the probability of selecting a 1-foot-square sample of material at random that on testing would have a breaking strength in excess of 2,265 psi.4.97 Refer to Exercise 4.96. Suppose that a new synthetic fabric has been developed that may have a different mean breaking strength. A random sample of 15 1-foot sections is obtained, and each section is tested for breaking strength. If we assume that the population standard deviation for the new fabric is identical to that for the old fabric, describe the sampling distribution forybased on random samples of 15 1-foot sections of new fabric
Une Entreprise œuvrant dans le domaine du multividéo donne l'opportunité à ses
programmeurs-analystes d'évaluer la performance des cadres supérieurs.
Voici les résultats obtenues (sur une échelle de 10 à 50) où 50 représentent une
excellente performance. 10 programmeurs furent sélectionnés au hazard pour
évaluer deux cadres. Un rapport Excel est également fourni.
Programmeurs
Cadre A Cadre B
1
34
36
2
32
34
3
18
19
33
38
19
21
21
23
7
35
34
8
20
20
9
34
34
10
36
34
Test d'égalité des espérances: observations pairées
A television news channel samples 25 gas stations from its local area and uses the results to estimate the average gas price for the state. What’s wrong with its margin of error?
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- You’re fed up with keeping Fido locked inside, so you conduct a mail survey to find out people’s opinions on the new dog barking ordinance in a certain city. Of the 10,000 people who receive surveys, 1,000 respond, and only 80 are in favor of it. You calculate the margin of error to be 1.2 percent. Explain why this reported margin of error is misleading.arrow_forwardYou find out that the dietary scale you use each day is off by a factor of 2 ounces (over — at least that’s what you say!). The margin of error for your scale was plus or minus 0.5 ounces before you found this out. What’s the margin of error now?arrow_forwardSuppose that Sue and Bill each make a confidence interval out of the same data set, but Sue wants a confidence level of 80 percent compared to Bill’s 90 percent. How do their margins of error compare?arrow_forward
- Suppose that you conduct a study twice, and the second time you use four times as many people as you did the first time. How does the change affect your margin of error? (Assume the other components remain constant.)arrow_forwardOut of a sample of 200 babysitters, 70 percent are girls, and 30 percent are guys. What’s the margin of error for the percentage of female babysitters? Assume 95 percent confidence.What’s the margin of error for the percentage of male babysitters? Assume 95 percent confidence.arrow_forwardYou sample 100 fish in Pond A at the fish hatchery and find that they average 5.5 inches with a standard deviation of 1 inch. Your sample of 100 fish from Pond B has the same mean, but the standard deviation is 2 inches. How do the margins of error compare? (Assume the confidence levels are the same.)arrow_forward
- A survey of 1,000 dental patients produces 450 people who floss their teeth adequately. What’s the margin of error for this result? Assume 90 percent confidence.arrow_forwardThe annual aggregate claim amount of an insurer follows a compound Poisson distribution with parameter 1,000. Individual claim amounts follow a Gamma distribution with shape parameter a = 750 and rate parameter λ = 0.25. 1. Generate 20,000 simulated aggregate claim values for the insurer, using a random number generator seed of 955.Display the first five simulated claim values in your answer script using the R function head(). 2. Plot the empirical density function of the simulated aggregate claim values from Question 1, setting the x-axis range from 2,600,000 to 3,300,000 and the y-axis range from 0 to 0.0000045. 3. Suggest a suitable distribution, including its parameters, that approximates the simulated aggregate claim values from Question 1. 4. Generate 20,000 values from your suggested distribution in Question 3 using a random number generator seed of 955. Use the R function head() to display the first five generated values in your answer script. 5. Plot the empirical density…arrow_forwardFind binomial probability if: x = 8, n = 10, p = 0.7 x= 3, n=5, p = 0.3 x = 4, n=7, p = 0.6 Quality Control: A factory produces light bulbs with a 2% defect rate. If a random sample of 20 bulbs is tested, what is the probability that exactly 2 bulbs are defective? (hint: p=2% or 0.02; x =2, n=20; use the same logic for the following problems) Marketing Campaign: A marketing company sends out 1,000 promotional emails. The probability of any email being opened is 0.15. What is the probability that exactly 150 emails will be opened? (hint: total emails or n=1000, x =150) Customer Satisfaction: A survey shows that 70% of customers are satisfied with a new product. Out of 10 randomly selected customers, what is the probability that at least 8 are satisfied? (hint: One of the keyword in this question is “at least 8”, it is not “exactly 8”, the correct formula for this should be = 1- (binom.dist(7, 10, 0.7, TRUE)). The part in the princess will give you the probability of seven and less than…arrow_forward
- please answer these questionsarrow_forwardSelon une économiste d’une société financière, les dépenses moyennes pour « meubles et appareils de maison » ont été moins importantes pour les ménages de la région de Montréal, que celles de la région de Québec. Un échantillon aléatoire de 14 ménages pour la région de Montréal et de 16 ménages pour la région Québec est tiré et donne les données suivantes, en ce qui a trait aux dépenses pour ce secteur d’activité économique. On suppose que les données de chaque population sont distribuées selon une loi normale. Nous sommes intéressé à connaitre si les variances des populations sont égales.a) Faites le test d’hypothèse sur deux variances approprié au seuil de signification de 1 %. Inclure les informations suivantes : i. Hypothèse / Identification des populationsii. Valeur(s) critique(s) de Fiii. Règle de décisioniv. Valeur du rapport Fv. Décision et conclusion b) A partir des résultats obtenus en a), est-ce que l’hypothèse d’égalité des variances pour cette…arrow_forwardAccording to an economist from a financial company, the average expenditures on "furniture and household appliances" have been lower for households in the Montreal area than those in the Quebec region. A random sample of 14 households from the Montreal region and 16 households from the Quebec region was taken, providing the following data regarding expenditures in this economic sector. It is assumed that the data from each population are distributed normally. We are interested in knowing if the variances of the populations are equal. a) Perform the appropriate hypothesis test on two variances at a significance level of 1%. Include the following information: i. Hypothesis / Identification of populations ii. Critical F-value(s) iii. Decision rule iv. F-ratio value v. Decision and conclusion b) Based on the results obtained in a), is the hypothesis of equal variances for this socio-economic characteristic measured in these two populations upheld? c) Based on the results obtained in a),…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Sampling Methods and Bias with Surveys: Crash Course Statistics #10; Author: CrashCourse;https://www.youtube.com/watch?v=Rf-fIpB4D50;License: Standard YouTube License, CC-BY
Statistics: Sampling Methods; Author: Mathispower4u;https://www.youtube.com/watch?v=s6ApdTvgvOs;License: Standard YouTube License, CC-BY