$7.($a$)$ You receive the prospectus of a growth fund started in the current year by a Princeton alum. What is the estimated RET $($excess return relative to the return of the benchmark market portfolio$)$ for this fund? $($b$)$ Are you confident that this fund will $$beat the market$,$ that is$,$ provide a return in excess of that of the benchmark market portfolio? Which standard error do we have to use in order to answer this question? $($c$)$ Suppose that you manage to identify a large number of growth funds started recently by Princeton graduates. By investing equally in all of these funds, how likely is it that your return will exceed that of the benchmark market portfolio by more than $1\mathrm{.}5$ percent? Which standard error did you use in your answer? $8.$ Suppose that you gain access to a much larger sample of random observations of the same variables that you have in the current dataset. Do you expect that any of your answers to Parts $($a$)($c$)$ of Question $8$ will change, and if so$,$ how? Discuss. $9.($a$)$ Based on the dataset, can you prove at the $5$ percent level of significance that among fund managers with the same educational background and same experience with the same fund, those managing growth and income funds are, on average, older? $($b$)$ Using the regression developed in part a$,$ provide an $80$ percent confidence interval for the average age difference between managers who graduated from the same college in the United States and have managed a growth fund for the same number of years but differ in whether or not they have an MBA. Are the $($otherwise comparable$)$ managers with MBAs younger or older, on average? Discuss $($conjecture$)$ why this is the case. $10.$ Based on your analysis of the case, which candidate do you support for AMBTPM$$s job