A stock analyst claims to have set up a mathematical technique for selecting high-quality mutual funds and promises that a client's portfolio will have a higher average 10 year annualized returns and lower volatility; that is a lower standard deviation. After 10 years, one of the analyst's twenty-four stock portoflios showed an average 10 year annualized 10 year return of 11.50% and a standard deviation of 10.17%. Then benchmarks for the type of mutual funds considered are a mean of 10.10% and a standard deviation of 15.67%.
a) Test at a 0.05 level of significance that the portfolio beat the benchmark for the mean.
b) Test at a 0.05 level of significance that the portfolio beat the benchmark for the standard deviation.
c) What assumptions did you make to solve this problem?