Question

In: Statistics and Probability

You don't need to be rich to buy a few shares in a mutual fund. The...

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.

-1.1 14.5 41.9 17.5 -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 ≈ 349.491 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 0.7 7.1 -1.8 -3.4 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 ≈ 136.708 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?

State the null and alternate hypotheses.

Ho: σ12 = σ22; H1: σ12 > σ22Ho: σ12 > σ22; H1: σ12 = σ22     Ho: σ22 = σ12; H1: σ22 > σ12Ho: σ12 = σ22; H1: σ12σ22



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


What are the degrees of freedom?

dfN
dfD

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population.     The populations follow independent normal distributions. The populations follow independent chi-square distributions. We have random samples from each population.


(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.100 0.050 < p-value < 0.100     0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.


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

Fail to reject the null hypothesis, there is sufficient evidence that the variance in percentage annual returns for mutual funds is greater in the aggressive-growth in small companies. Reject the null hypothesis, there is insufficient evidence that the variance in percentage annual returns for mutual funds is greater in the aggressive-growth in small companies.     Reject the null hypothesis, there is sufficient evidence that the variance in percentage annual returns for mutual funds is greater in the aggressive-growth in small companies. Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage annual returns for mutual funds is greater in the aggressive-growth in small companies.

Solutions

Expert Solution

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: Ho: σ12 = σ22; H1: σ12 > σ22

b) Sample test statistic = 2.56

dfN = 20

dfD = 20

The populations follow independent normal distributions. We have random samples from each population.

c) 0.010 < p-value < 0.025

d) At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

e) Reject the null hypothesis, there is sufficient evidence that the variance in percentage annual returns for mutual funds is greater in the aggressive-growth in small companies.


Related Solutions

You don't need to be rich to buy a few shares in a mutual fund. The...
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 14.5 41.9 17.5 -16.9 4.4 32.6 -7.3 16.2 2.8...
You don't need to be rich to buy a few shares in a mutual fund. The...
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. -1.2 14.5 41.1 17.3 -16.5 4.4 32.6 -7.3 16.2 2.8...
You don't need to be rich to buy a few shares in a mutual fund. The...
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. -1.3 14.8 41.3 17.5 -16.6 4.4 32.6 -7.3 16.2 2.8...
You don't need to be rich to buy a few shares in a mutual fund. The...
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. -1.1 14.6 41.9 17.9 -16.4 4.4 32.6 -7.3 16.2 2.8...
You don't need to be rich to buy a few shares in a mutual fund. The...
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 14.4 41.4 17.1 -16.5 4.4 32.6 -7.3 16.2 2.8...
You don't need to be rich to buy a few shares in a mutual fund. The...
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. -1.4 14.3 41.5 17.4 -16.5 4.4 32.6 -7.3 16.2 2.8...
You don't need to be rich to buy a few shares in a mutual fund. The...
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 14.6 41.7 17.3 -16.9 4.4 32.6 -7.3 16.2 2.8...
At the beginning of the year, you buy 800 shares in Muleshoe Mutual Fund, which currently...
At the beginning of the year, you buy 800 shares in Muleshoe Mutual Fund, which currently has a NAV of $48.10. The fund has a front-end load of 1.8%. Over the year, the fund distributed capital gains of $1.75 per share and dividend distributions of $1.42. At the end of the year, the NAV was at $54.47 and the offer price was at $55.45. A. If you sell after one year, what is your HPR? B. Recalculate your HPR, assuming...
Linard wants to buy shares in a mutual fund. The current NAV is $44.18. He looks...
Linard wants to buy shares in a mutual fund. The current NAV is $44.18. He looks up fund characteristics on Robinhood and found the following: Operating Expenses: 1.10%, Front-end loan: 0.80%, back-end loan (if exiting after one year): 1.70%, and 12b-1 fees of 0.10%. What would be his rate of return if he buys this fund today and sells after one year if the fund returns 15% over this period?
) What is a Mutual Fund? A. A pool of securities you can buy as an...
) What is a Mutual Fund? A. A pool of securities you can buy as an investment B. A fund used by companies to raise capital C. A fund that follows an index you can buy like a stock D. A type of high-interest bank account Which is a characteristic of open-ended mutual funds? A. Shares trade throughout the day B. There is a limit to the size of the fund C. Investors typically hold fractions of shares D. They...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT