A life insurance salesman believes that the mean age of people who buy their first life insurance plan is less than 35. To test his belief, he takes a random sample of 15 customers who have just purchased their first life insurance. Their ages are shown, and assume to be normally distributed: 42, 43, 28, 34, 30, 36, 25, 29, 32, 33, 27, 30, 22, 37, and 40. (Please use a statistical software package to solve the problems) a. Can we conclude at the 5% significance level that the insurance salesman is correct? (1) b. Construct a 95% confidence interval of the mean age of people who buy their first life insurance plan. Interpret the confidence interval in the context of the problem. (1) c. Check to ensure that the assumption of the statistical method used in parts (a) and (b) is satisfied. (1)