The average annual total return for U.S. Diversified Equity mutual funds from 1999 to 2003
was 4.1% (BusinessWeek, 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 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 mid-cap growth funds provides a mean return of 3.4%. Assume
the population standard deviation for mid-cap growth funds is known from previous
studies to be s 2%. Use the sample results to compute the test statistic and p-value
for the hypothesis test.
c. At a .05, what is your conclusion?