One of the major U.S. tire makers wishes to review its warranty for their rainmaker tire. The warranty is for 40,000 miles. The tire company believes that the tire actually lasts more than 40,000 miles. A
Sample 49 tires revealed that the mean number of miles is 45,000 miles with a standard deviation of
15,000 miles. Test the hypothesis with a 0.05 significance level.
A) At a 5% level of significance, our decision is to reject the null hypothesis. The tires last more than 40 000 miles.
B) At a 5% level of significance, our decision is to accept the null hypothesis. The tires last 40,000 miles.
C) At a 5% level of significance, we should have used the t-test, rather than the z-test.
D) None of these statements is correct.

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean tire life is 40,000 miles. The alternative hypothesis is that it is more than 40,000 miles. Using a z-test, the calculated z-value is 2.33, which is greater than the critical z-value of 1.645 for a one-tailed test at the 0.05 significance level. Therefore, we reject the null hypothesis.

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