Question

The U.S. Department of Transportation requires tire manufacturers to provide tire performance on the sidewall of the tire to better inform prospective customers when making a purchase.One very important measure of tire performance is the tread wear index, which indicates the tire's resistance to tread wear compared with a tire graded with a base of 100. This means that a tire with a grade of 200 should last twice as long, on average, as a tired graded with a base of 100. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claim "graded 200" on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. A) Assuming that the population of tread wear indexes is normally distributed, construct a 95% confidence interval estimate of the population mean tread index for tires produced by this manufacturer under this brand name. B) Do you think that the consumer organization should accuse the manufacturer of producing tires that do not think meet the performance information provided on the sidewall of the tire? Explain. C) Explain why an observed tread wear index of 210 for a particular tire is not usual, even though it is outside the confidence interval developed in (a).

Answer 1