In Exercise 2.44 you learned that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The table below lists 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).

a. Find a 90% confidence interval for the average annualized percentage return on investment of all stock screeners provided by AAII. Interpret the result.
b. Recall that a negative annualized return reflects a stock portfolio that performed worse than the S&P 500. On average, do the AAII stock screeners perform worse or better than the S&P 500? Explain.
c. What assumption about the distribution of the annualized percentage returns on investment is required for the inference, part b, to be valid? Is this assumption reasonably satisfied?

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