A government\'s department of transportation requires tire manufacturers to prov

Question

A government's department of transportation requires tire manufacturers to provide performance information on tire sidewalls to help prospective buyers make their purchasing decisions. One very important piece of information is the tread wear index, which indicates the tire's resistance to tread wear. A tire with a grade of 200 should last twice as long, on average, as a tire with a grade of 100. A consumer organization wants to test 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 195.8 and a sample standard deviation of 21.4. Complete parts (a) and (b) below. Is there evidence that the population mean amount is different from a grade of 200? (Use a 0.01 level of significance.) State the null and alternative hypotheses. H_0 mu = H_1 mu =

Explanation / Answer

Answers to the question:

n=18
Sample mean = 195.8
Ssample deviation = 21.4

Pop. mean = 200

So,

Ho : Mu=200
Ha : Mu!=200

t ( we use t as n<30)= (195.8-200)/(21.4/sqrt(18)) = -.832

Converting this 2 tailed t value of -.832 into p value with df = 18-1=17 we have:

p = .42 which is much larger than .01

So, we conclude that we will not reject Ho and conclude "The population mean is actually 200)

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