The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of a tire to better inform prospective customers as they make purchasing decisions. 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. A tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims "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 for the population mean tread wear 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 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 unusual, even though it is outside the confidence interval developed in (a).