The U.S. Department of Transportation requires tire manufacturers to provide tir

Question

The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of the tire so that a prospective customer can be better informed when making a purchasing decision. 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. Suppose that a consumer organization wants to estimate the actual tread wear index of a brand name of tires graded 200 that are produced by a certain manufacturer. A random sample of 18 of these tires produced a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. Assuming that the population of tread wear indices is normally distributed, compute a 95% confidence interval estimate for the population mean tread wear index for tires produced by this manufacturer under this brand name. Place your answer, rounded to 2 decimal places, in the blanks Lower Limit=; Upper Limit=

Explanation / Answer

n = 18
sample mean, x = 195.3
sample standard deviation, s = 21.4
standard error, e = s/?n = 5.044

z at 95% = 1.96
confidence interval, CI= x ± ze = 195.3 ± 1.96 x5.044 = (185.41, 205.17)
Therefore, Lower Limit = 185.41 and Upper Limit = 205.17

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