A study was undertaken to evaluate how stocks are affected by being listed in the Standard & Poor's 500 Index. The aim of the study was to assess average excess returns for these stocks, above returns on the market as a whole. The average excess return on any stock is zero because the "average" stock moves with the market as a whole.
As part of the study, a random sample of 13 stocks newly included in the S&P 500 Index was selected. Before the sampling takes place, we allow that average "excess return" for stocks newly listed in the Standard & Poor's 500 Index may be either positive or negative; therefore, we want to test the null hypothesis that average excess return is equal to zero versus the alternative that it is not zero.
If the excess return on the sample of 13 stocks averaged 3.1% and had a standard deviation of 1%, do you believe that inclusion in the Standard & Poor's 500 Index changes a stock's excess return on investment, and if so, in which direction? Explain. Use α = 0.05.