The Beta coefficients of stocks are measure of their volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 generally bear greater risk (more volatile) than the market, whereas stocks with beta coefficients less than one are less risky (less volatile) than the overall market (Sharpe and Alexander 1990). A random sample of 16 utility stocks was selected at the end of February 2012, and the mean and standard deviation of the beta coefficients were calculated: Sample
Mean = .80, Sample Standard Deviation = .40.
(a) Set up the appropriate null and alternative hypotheses to test that the average of utility stocks is less risky than the market as a whole.
(b) Perform the appropriate statistical test and explain your conclusion. Use alpha = .01.