The trading skills of institutional stock 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-trip trades 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-trip trades is positive, then the population of institutional investors is considered to have performed successfully.
a. Specify the null and alternative hypotheses for determining whether the population of institutional investors performed successfully.
b. Find the rejection region for the test using α = .05.
c. Interpret the value of a in the words of the problem.
d. A Minitab printout of the analysis is shown below. Locate the test statistic and p-value on the printout.
e. Give the appropriate conclusion in the words of the problem.

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Test of u = 0 vs > 0 Mean StDev sE Mean 95 Lower Bound 0.624 1.919 4.73 0.000 200 2.950 8.820