Question: A country club has various “levels” of memberships: social, junior, full, and senior. Based on a sample of 101 “full” members, the average amount spent in the club’s restaurant in a given month was $169 with a standard deviation of $33. In a different sample of 61 “senior” members, the average amount spent in the club’s restaurant was $186 with a standard deviation of $26.

a) Using the 5% level of significance, test whether there is a difference in the average amount spent by “senior” members compared with “full” members. (15)

b) What is the p-value of this test? (5)

c) For forecasting purposes, the manager of a country club thinks wants to know whether the variance of the amount spent in the club’s restaurant differs by type of membership (obviously it is easier to forecast future club revenue if the variance is lower). Test the hypothesis at the 1% level of significance that the variance of the amount spent by “full” member is significantly higher than the variance of the amount spent by “senior” members. (15)