Trading skills of institutional investors. Managers of stock portfolios make decisions as to what stocks to buy and sell in a given quarter. The trading skills of these institutional investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on "round-trip" trades, i.e., trades in which the same stock was both bought and sold in the same quarter. Consider a random sample of 200 round trips made by institutional investors. Suppose the sample mean rate of return is 2.95% and the sample standard deviation is 8.82%. If the true mean rate of return of round-trips is positive, then the population of institutional investors is considered to have preformed successfully.

a) Specify the null and alternative hypotheses for determining whether the population of institutional investors preformed successfully.

b) Find the rejection region for the test using alpha=0.05.

c) Interpret the value of alpha in the words of the problem.

d) Give the appropriate conclusion in the words of the problem.