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
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
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