Question: The manufacturer of a certain brand of auto batteries claims the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 36 such batteries and found the mean life for this sample is 43.75 months with a standard deviation of 4.5 months.

a. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months.

b. Would you reject the manufactures claim at a 5% significance level? Explain your answer.