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An engineer wishes to compare the wearing qualities of two types of automobile tires, A and B. tire of type A and one of type B are randomly assigned and mounted on the rear wheels of eac eight automobiles. The automobiles are then operated for a specified number of kilometers, and amount of wear is recorded for each tire. The results are recorded in the following table. Automobile 1 2 7 10 11 Amount of wear Tire A 10.5 9.7 12.4 9.7 8.7 11.5 10.8 9.9 9.0 10.3 12.0 Tire B 10.2 9.3 11.9 9.2 8.3 11.2 10.4 9.5 8.8 9.0 10.5 Assume that the distributions for both populations are normally distributed and a = 0.05. Answer following questions using the data given in the above table. You may use any statistical output f any software to help you solve the following problems. a) Check the assumption of variances that is required to test the difference in the mean wear for two types of tires. You may use either the confidence interval or hypothesis test to check on assumption of variances based on the data above. Show your working, justification and conclu clearly. b) Generate the statistical output(s) to test if there is a difference in the mean wear for the two ty of tires. Your output(s) should include the values of the confidence interval, test statistic an value. Answer the following questions based on your generated output(s).

An engineer wishes to compare the wearing qualities of two types of automobile tires, A and B. tire of type A and one of type B are randomly assigned and mounted on the rear wheels of eac eight automobiles. The automobiles are then operated for a specified number of kilometers, and amount of wear is recorded for each tire. The results are recorded in the following table. Automobile 1 2 7 10 11 Amount of wear Tire A 10.5 9.7 12.4 9.7 8.7 11.5 10.8 9.9 9.0 10.3 12.0 Tire B 10.2 9.3 11.9 9.2 8.3 11.2 10.4 9.5 8.8 9.0 10.5 Assume that the distributions for both populations are normally distributed and a = 0.05. Answer following questions using the data given in the above table. You may use any statistical output f any software to help you solve the following problems. a) Check the assumption of variances that is required to test the difference in the mean wear for two types of tires. You may use either the confidence interval or hypothesis test to check on assumption of variances based on the data above. Show your working, justification and conclu clearly. b) Generate the statistical output(s) to test if there is a difference in the mean wear for the two ty of tires. Your output(s) should include the values of the confidence interval, test statistic an value. Answer the following questions based on your generated output(s).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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An engineer wishes to compare the wearing qualities of two types of automobile tires, A and B. One tire of type A and one of type B are randomly assigned and mounted on the rear wheels of each of eight automobiles. The automobiles are then operated for a specified number of kilometers, and the amount of wear is recorded for each tire. The results are recorded in the following table. Automobile 1 2 SAWN 3 7 8 9 10 11 Amount of wear Tire A 10.5 9.7 12.4 9.7 8.7 11.5 10.8 9.9 9.0 10.3 12.0 Tire B 10.2 9.3 11.9 9.2 8.3 11.2 10.4 9.5 8.8 9.0 10.5 Assume that the distributions for both populations are normally distributed and a = 0.05. Answer the following questions using the data given in the above table. You may use any statistical output from any software to help you solve the following problems. a) Check the assumption of variances that is required to test the difference in the mean wear for the two types of tires. You may use either the confidence interval or hypothesis test to check on the assumption of variances based on the data above. Show your working, justification and conclusion clearly. b) Generate the statistical output(s) to test if there is a difference in the mean wear for the two types of tires. Your output(s) should include the values of the confidence interval, test statistic and p- value. Answer the following questions based on your generated output(s). c) Use the output(s) in (b), answer the following questions. i) Verify the values of the confidence interval for the difference in two populations in your output by calculation. ii) Conduct a hypothesis test to see if there is a difference in the mean wear for the two types of tires. Conclude your test clearly in context of the problem. d) Based on the hypothesis test in (c)(ii), explain in context of the problem whether you have committed the Type I or Type II error.
Transcribed Image Text:An engineer wishes to compare the wearing qualities of two types of automobile tires, A and B. One tire of type A and one of type B are randomly assigned and mounted on the rear wheels of each of eight automobiles. The automobiles are then operated for a specified number of kilometers, and the amount of wear is recorded for each tire. The results are recorded in the following table. Automobile 1 2 SAWN 3 7 8 9 10 11 Amount of wear Tire A 10.5 9.7 12.4 9.7 8.7 11.5 10.8 9.9 9.0 10.3 12.0 Tire B 10.2 9.3 11.9 9.2 8.3 11.2 10.4 9.5 8.8 9.0 10.5 Assume that the distributions for both populations are normally distributed and a = 0.05. Answer the following questions using the data given in the above table. You may use any statistical output from any software to help you solve the following problems. a) Check the assumption of variances that is required to test the difference in the mean wear for the two types of tires. You may use either the confidence interval or hypothesis test to check on the assumption of variances based on the data above. Show your working, justification and conclusion clearly. b) Generate the statistical output(s) to test if there is a difference in the mean wear for the two types of tires. Your output(s) should include the values of the confidence interval, test statistic and p- value. Answer the following questions based on your generated output(s). c) Use the output(s) in (b), answer the following questions. i) Verify the values of the confidence interval for the difference in two populations in your output by calculation. ii) Conduct a hypothesis test to see if there is a difference in the mean wear for the two types of tires. Conclude your test clearly in context of the problem. d) Based on the hypothesis test in (c)(ii), explain in context of the problem whether you have committed the Type I or Type II error.
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