All season tire claim math problem?

The manufacturer of a particular all season tire claims that the tires last for 22,000 miles. After purchasing the tires you discover that yours did not last the full 22,000 miles. Suppose that a sample of 100 tires made by them lasted on average 21,819 miles with a standard deviation of 1,295 miles. Is there sufficent evidence to refute the manufactuers claim that the tires last 22,000?


Let a = 0.05. assume that the population standard deviation is o = 1300


a. define the null and the alternate hypothesis


b. find the appropriate rejection region


c. compute the test static


d. what is your conclusion? Explain

All season tire claim math problem?
a. null: u = 22,000 alt: u %26lt; 22000


b. since alpha = .05, and it is left-tailed test, the critical value is z = -1.645 and the rejection region is z %26lt; -1.645





c. test statistic: z = (21819-22000)/ (1295/sqrt(100))


z = -181/129.5 = -1.40 (You get -1.39 if use the pop st. dev of 1300)


d. Since -1.40 is not less than -1.645 it is not in the rejection region and therefore you do not reject the null hypothesis. There is not sufficient evidence to refute the manufacturer's claim.

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