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10.9 A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars this mean is $3850. Assume that the standard deviations for the two populations are $800 and $1000, respectively a. Construct a 99% confidence interval for the difference between the two population means b. Using a 1% significance level, can you conclude that such mean repair costs are different for these two types of cars? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain

10.9 A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars this mean is $3850. Assume that the standard deviations for the two populations are $800 and $1000, respectively a. Construct a 99% confidence interval for the difference between the two population means b. Using a 1% significance level, can you conclude that such mean repair costs are different for these two types of cars? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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10.9 A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars this mean is $3850. Assume that the standard deviations for the two populations are $800 and $1000, respectively a. Construct a 99% confidence interval for the difference between the two population means b. Using a 1% significance level, can you conclude that such mean repair costs are different for these two types of cars? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain
Transcribed Image Text:10.9 A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYS are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars this mean is $3850. Assume that the standard deviations for the two populations are $800 and $1000, respectively a. Construct a 99% confidence interval for the difference between the two population means b. Using a 1% significance level, can you conclude that such mean repair costs are different for these two types of cars? c. What would your decision be in part b if the probability of making a Type I error were zero? Explain
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