Investing: Mutual Funds You don’t need to be rich to buy a few shares in a mutual fund. The question is,

“How reliable are mutual funds as investments?” That depends on the type of fund you buy. The following data are based on information taken from Morningstar, a mutual fund guide available in most libraries. A random sample of percentage annual returns for mutual funds holding stocks in aggressive-growth small companies is shown next.

−1.8 14.3 41.5 17.2 −16.8 4.4 32.6 −7.3 16.2 2.8 34.3

−10.6 8.4 −7.0 −2.3 −18.5 25.0 −9.8 −7.8−24.6 22.8 Use a calculator to verify that s2 < 348.43 for the sample of aggressive-growth small company funds.

Another random sample of percentage annual returns for mutual funds holding value (i.e., market underpriced) stocks in large companies is shown next.

16.2 0.3 7.8 −1.6 −3.8 19.4 −2.5 15.9 32.6 22.1 3.4

−0.5 −8.3 25.8 −4.1 14.6 6.5 18.0 21.0 0.2 −1.6 Use a calculator to verify that s2 < 137.31 for value stocks in large companies.

Test the claim that the population variance for mutual funds holding aggressive-growth small stocks is larger than the population variance for mutual funds holding value stocks in large companies. Use a 5%

level of significance. How could your test conclusion relate to the question of reliability of returns for each type of mutual fund?

please provide the following information.

(a) What is the level of significance? State the null and alternate hypotheses.

(b) Find the value of the sample F statistic. What are the degrees of freedom? What assumptions are you making about the original distribution?

(c) Find or estimate the P-value of the sample test statistic.

(d) Based on your answers in parts

(a) through (c), will you reject or fail to reject the null hypothesis?

(e) Interpret your conclusion in the context of the application.AppendixLO1