The 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).

RETURN 9 -0.1 -1.6 14.6 16 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1

a. compute the mean and standard deviation of the annualized percentage return on investment b. Find a 90% confidence interval for the average annualized percentage return on investment of all stock screeners provided by AAII. Interpret the result. c. A positive annualized return reflects a stock portfolio that performed better than the S&P 500. On average, do the AAII stock screeners perform better than the S&P 500? Please use results from a to explain. d. Conduct a hypothesis test to support the claim that AAII stock screeners perform better than the S&P 500. Report the P-value.