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 14.3 41.9 17.9 -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 ≈ 350.311 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 0.4 7.4 -1.3 -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 ≈ 136.430 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: ?12 = ?22; H1: ?12 > ?22Ho: ?12 > ?22; H1: ?12 = ?22 Ho: ?22 = ?12; H1: ?22 > ?12Ho: ?12 = ?22; H1: ?12 ≠ ?22 (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 independent normal distributions.The populations follow independent normal distributions. We have random samples from each population. The populations follow dependent normal distributions. We have random samples from each population.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 > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-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 ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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.

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 14.3 41.9 17.9 -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 ≈ 350.311 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 0.4 7.4 -1.3 -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 ≈ 136.430 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: ?12 = ?22; H1: ?12 > ?22Ho: ?12 > ?22; H1: ?12 = ?22 Ho: ?22 = ?12; H1: ?22 > ?12Ho: ?12 = ?22; H1: ?12 ≠ ?22 (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 independent normal distributions.The populations follow independent normal distributions. We have random samples from each population. The populations follow dependent normal distributions. We have random samples from each population.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 > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-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 ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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.

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Description: 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 availa

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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.

-1.2	14.3	41.9	17.9	-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 ≈ 350.311 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	0.4	7.4	-1.3	-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 ≈ 136.430 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.

H_o: ?₁² = ?₂²; H₁: ?₁² > ?₂²H_o: ?₁² > ?₂²; H₁: ?₁² = ?₂² H_o: ?₂² = ?₁²; H₁: ?₂² > ?₁²H_o: ?₁² = ?₂²; H₁: ?₁² ≠ ?₂²

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

What are the degrees of freedom?

df_N
df_D

What assumptions are you making about the original distribution?

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

p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.001 < p-value < 0.010p-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 ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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