# A stock analyst claims to have devised a mathematical technique for selecting high-quality mutual funds and promises

## Question:

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 μ 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 H0: μ = 10.1 versus H1: μ > 10.1.

(b) Let σ 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 H0: σ = 15.67 versus H1: σ < 15.67.

Mutual Funds
Mutual funds are like a pool of funds gathered by different small investors that have simalar investment perspective about returns on their investments. These funds are managed by professional investment managers who act smartly on behalf of the...
Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...
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