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? This depends on the type of fund you buy. The following data are based on information taken from 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 below. -1.6 14.5 41.4 17.1 -16.6 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 ≈ 347.545 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 below. 16.3 0.8 7.1 -1.3 -3.5 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 ≈ 136.391 for value stocks in large companies. Test the claim that the population variance for mutual funds holding aggressive-growth in small companies 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? (a) What is the level of significance? (b) Find the value of the sample F statistic. (Use 2 decimal places.) What are the degrees of freedom? dfN dfD

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Author:Amos Gilat

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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? This depends on the type of fund you buy. The following data are based on information taken from 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 below.

-1.6	14.5	41.4	17.1	-16.6	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 ≈ 347.545 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 below.

16.3	0.8	7.1	-1.3	-3.5	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 ≈ 136.391 for value stocks in large companies.

Test the claim that the population variance for mutual funds holding aggressive-growth in small companies 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?

(a) What is the level of significance?

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

df_N
df_D

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