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) 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 the tires meet the performance information. 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).