Question 7

In a research of tire performance by Department of Industrial Engineering, they claimed that 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 tire graded with a base of 100. They also estimate the actual tread wear index of a ABC 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 of the population mean tread wear index for tires.

b) Do you think that Department of Industrial Engineering should accuse the manufacturer of ABC tires that do not meet the performance information provided on the sidewall of the tire?

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).