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. -1.5 14.4 41.3 17.4 -16.2 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 ≈ 346.508 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. 16.1 0.9 7.4 -1.8 -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 ≈ 136.999 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) Find the value of the sample F statistic. (Use 2 decimal places.) B) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.) C) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
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.
| -1.5 | 14.4 | 41.3 | 17.4 | -16.2 | 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 ≈ 346.508 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.
| 16.1 | 0.9 | 7.4 | -1.8 | -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 ≈ 136.999 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) Find the value of the sample F statistic. (Use 2 decimal places.)
B) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)
C) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
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