7.5.16. A stock analyst claims to have devised a mataematica.l technique for selecting high
quality mutual funds and promises that a client's portfolio will have higher average
10-ye.ar annualized returns and lower volatility; that is, a smaller standard deviation. Af ter 10 years, ·one of the analyst's 24-stock portfolios showed an average 10-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 devia tion of 15.67%.
(a) Let µbe the mean for a 24-stock portfolio selected by the analys1'smethod. Test at the 0.0S level that the portfolio beat the benchmark; that is, test Ho:µ = 10.1
versus Hi: µ => 10.l.
(b) Let a be the standard deviation for a 24-stock portfolio selected by the analyst's method. Test at the 0.05 Level that the portfolio be.at the benchmark; that is, test
Ho: a = 15.67 versus H1: a 15.67.
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