Chapter 7.5, Problem 17Q

A stock analyst claims to have devised a mathematical technique for selecting high-quality mutual funds and promises that a client’s portfolio will have higher average ten-year annualized returns and lower volatility; that is, a smaller standard deviation. After ten years, one of the analyst’s twenty-four-stock portfolios showed an average ten-year annualized return of 11.50% and a standard deviation of 10.17%. The benchmarks for the type of funds considered are a mean of 10.10% and a standard deviation of 15.67%.

• (a) Let $\mu$ be the mean for a twenty-four-stock portfolio selected by the analyst’s method. Test at the 0.05 level that the portfolio beat the benchmark; that is, test $H_0:\mu =10.1$ versus $H_1:\mu >10.1$.

• (b) Let $\sigma$ be the standard deviation for a twenty-four-stock portfolio selected by the analyst’s method. Test at the 0.05 level that the portfolio beat the benchmark; that is, test $H_0:\sigma =15.67$ versus $H_1:\sigma <15.67$.