Question

Shareholders and bankers use the standard deviation of the monthly percentage return for a mutual fund as a measure of the risk for the fund. For instance, a fund that has a larger standard deviation is considered riskier than a fund with a lower standard deviation. The standard deviation for the American Century Equity Growth fund and the standard deviation of the Fidelity Growth Discovery fund were recently reported to be 15.0% and 18.9% respectively. Assume that these standard deviations are based on a sample of 31 months of returns for the Fidelity Growth Discovery fund and 61 months of returns for the American Century Equity Growth fund.

Using a significance level of α = .05, do the sample results support the conclusion that the Fidelity fund has a larger population variance than the American Century fund? Do a complete and appropriate hypothesis test using the critical value approach and the 5-step procedure.

Answer 1

Step 1:

H0: Null Hypothesis: ( the Fidelity fund does not have a larger population variance than the American Century fund)

HA: Alternative Hypothesis: ( the Fidelity fund has a larger population variance than the American Century fund) (Claim)

Step 2:

=0.05

Step 3:

Degrees of Freedom (30,60)

One Tail - Right Side Test

Critical Value of F = 1.649

Step 4:

Test Statistic is given by:

Step 5:
Since calculated value of F = 1.5876 is less than critical value of F = 1.649, the difference isnot significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that the Fidelity fund has a larger population variance than the American Century fund.