(a) Based on the dataset, can you prove at the 5 percent level of significance that among fund managers with the same educational background and same experience with the same fund, those managing growth and income funds are, on average, older? (b) Using the regression developed in part a, provide an 80 percent confidence interval for the average age difference between managers who graduated from the same college in the United States and have managed a growth fund for the same number of years but differ in whether or not they have an MBA. Are the (otherwise comparable) managers with MBAs younger or older, on average? Discuss (conjecture) why this is the case.