Recall, from Exercise 6.36, that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether m, the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 394.

a. State H0 and Ha for this test.
b. Locate the values of x and s on the printout, and then use these values to compute the test statistic. Verify that your calculation is correct by comparing it with the test statistic value shown on the printout.
c. Locate the observed significance level (p-value) on the printout.
d. Give the appropriate conclusion if you test using α = .05.
e. What assumption about the data must hold in order for the inference derived from the test to be valid?

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9.0 -.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1 One-Sampte Statistics Mean Std. Deviation Std. Error Mean RADON 12 3642 50 4486.929 One-Sample Test Test Value 6000 1295.265 95% Confidence Interval of the Mean Difference Sig (2-tailed) df 11 -1.820 .090 Difference Lower Upper 493.36 RADON -2357.500 -5208.36