The US. Department of Transportation requires t!:,' manufacturers 10 prO\'ide tire performance information ,.'Il the sidewall of a tire to better inform prospective custonwr, as they make purchasing decisions. Olle very import",.! measure of tire performa

Question no 8.17

The US. Department of Transportation requires t!:,'

manufacturers 10 prO\'ide tire performance information ,.'Il

the sidewall of a tire to better inform prospective custonwr,

as they make purchasing decisions. Olle very import",.!

measure of tire performance is the tread wear index. whtd:

indicates tilt' tire's resistance 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