Trading skills of institutional investors. The Journal of Finance (Apr. 2011) published the results of an analysis of trading skills of institutional investors. The study focused on “round-trip” trades, i.e., trades in which the same stock was both bought and sold in the same quarter. In a random sample of 200 round-trip trades made by institutional investors, the sample standard deviation of the rates of return was 8.82%. One property of a consistent performance of institutional investors is a small variance in the rates of return of round-trip trades, say, a standard deviation of less than 10%.

a. Specify the null and alternative hypotheses for determining whether the population of institutional investors performs consistently.

b. Find the rejection region for the test using a = .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.

f. What assumptions about the data are required for the inference to be valid?

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Test and CI for One Variance Method Null hypothesis Alternative hypothesis Sigma = 10 Sigma < 10 The chi-square method is only for the normal distribution. The Bonett method cannot be calculated with summarized data. Statistics N StDev Variance 200 8.82 Tests 77.8 Test Method Statistic DE P-Value Chi-Square 154.81 199 0.009