Question: A trucking firm suspects that the mean lifetime of a certain tire it uses is less than 32,000 miles. To check the claim, the firm randomly selects and tests 25 of these tires and gets a mean lifetime of 31,900 miles with a standard deviation of 1150 miles. At α = .05, test the trucking firm's claim.

a. Determine which test statistic you will use: the standard normal distribution, or the student's t distribution. Explain why you chose this test statistic.

b. Establish the null and alternative hypotheses, state the claim.

c. Test the claim at α = .05 and discuss your results, should you reject or not reject the null hypothesis, should you reject or except the claim.