The average annual total return for U. Diversified Equity mutual funds from 1999 to 2003 was 4.1% (Business Week, January 26, 2004).

The average annual total return for U.S. Diversified Equity mutual funds from 1999 to 2003 was 4.1% (Business Week, January 26, 2004). A researcher would like to conduct a hypothesis test to see whether the returns for mid-cap growth funds over the same period are significantly different from the average for U.S. Diversified Equity funds.
a) Formulate the null and alternative hypotheses that can be used to determine whether the mean annual return for mid-cap growth funds differ from the mean for U. S. Diversified Equity funds.
b) A sample of 40-midcap growth funds provides a mean return of (3.4%). Assume the population standard deviation for a mid-cap growth
funds is known from previous studies to be a standard deviation of 2%. Use the sample results to compute the test statistic and p-value for the hypothesis test.
c) At alpha criteria of .05, what’s your conclusion?
 
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