Question: 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 that manufacturer lasted on average 21,819 miles with a sample standard deviation of 1,295 miles. Is there sufficient evidence to refute the manufacturer's claim that the tires last 22,000 miles? Let a = 0.05. Assume that the population standard deviation is \(\sigma \) = 1300.

a. Define the null and alternative hypotheses.

b. Find the appropriate rejection region.

c. Compute the test statistic.

d. What is your conclusion? Explain.