Question

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.

-1.8	14.5	41.9	17.4	-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 ≈ 349.854 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.

16.2	0.6	7.9	-1.9	-3.3	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 ≈ 136.756 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?

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

Answer 1

For Sample 1 :

Sample variance using excel function VAR.S, s₁² = 349.8541

Sample size, n1 = 21

For Sample 2 :

Sample variance using excel function VAR.S, s₂² = 136.7563

Sample size, n2 = 21

--

Null and alternative hypothesis:

Hₒ : σ₁² = σ₂²

H₁ : σ₁² > σ₂²

Test statistic:

F = s₁² / s₂² = 349.8541 / 136.7563 = 2.56

Degree of freedom:

df₁ = n₁-1 = 20

df₂ = n₂-1 = 20

P-value = F.DIST.RT(2.56, 20, 20) = 0.021

Conclusion:

As p-value < α, we reject the null hypothesis.