The U.S. Department of Transportation requires tiremanufacturers to provide tire

Question

The U.S. Department of Transportation requires tiremanufacturers to provide tire performance information on thesidewall of the tire to better inform prospective customers whenmaking purchasing decisions. One very important measure of tireperformance is the tread wear index, which indicates thetire’s resistance to tread wear compared with a tire gradedwith a base of 100. This means that a tire with a grade of 200should last twice as long, on average, as a tire graded with a baseof 100. A consumer organization wants to estimate the actual treadwear index of a brand name of tires graded 200 that are produced bya certain manufacturer. A random sample of n;= 18 indicates asample mean thread wear index of 95.3 and a sample standarddeviation of 21.4. ,

a. Assuming that the population of tread wear indices isnormally distributed, construct a 95% confidence interval estimateof the population mean tread wear index for tires produced by thismanufacturer under this for tires produce

b. Do you think that the consumer organization should accuse themanufacturer of producing tires that do not meet the performanceinformation provided on the side wall the performance inform

c. Explain why an observed tread wear index of 210 for aparticular tire is not unusual, even though it is outsideparticular tire is not unusual, even though it is outside theconfidence interval developed in (a).

Explanation / Answer

a) n = 18 sample mean, x = 95.3 sample standard deviation, s = 21.4 standard error, e = s/n = 5.044 z = 1.96 confidence interval, CI= x ± ze = 95.3 ± 1.96 x5.044 = (85.41, 105.19)

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