The following table gives the age (in years) of 36 randomly selected U.S. millionaires. The sample mean is58.53 years. Assume that the standard deviation of the ages of all U.S. millionaires is 13.0 years.

(a) Test at the 5% significance level whether the average year of age of all U.S. millionaires is below 60 years. (8 marks)

(b) What is the P-value of the hypothesis test in part (a)? (2 marks)

(c) Obtain and interpret a 90% two-sided confidence interval for the population mean age of all U.S. millionaires. (6 marks)

(d) Does the interval in part (c) give evidence that the average age of all U.S. millionaires differs from 60 years? Explain your answer. (3 marks)

(e) Determine the number of millionaires who should be picked to guarantee that the error made in estimatingu by sample mean is at most 0.5 years with 98% confidence. (4 marks)