You may need to use the appropriate technology to answer this question. Investors commonly use the standard deviation of the monthly percentage return for a mutual fund as a measure of the risk for the fund; in such cases, a fund that has a larger standard deviation is considered more risky than a fund with a lower standard deviation. The standard deviation for a certain fund, referred to as Fund A, and the standard deviation for a second fund, Fund B, were recently reported to be 14.0% and 18.9%, respectively. Assume that each of these standard deviations is based on a sample of 60 months of returns. Do the sample results support the conclusion that the Fund B has a larger population variance than Fund A? (Assume that ? = 0.05.) State the null and alternative hypotheses. H0: ?12 ≤ ?22 Ha: ?12 > ?22 H0: ?12 = ?22 Ha: ?12 ≠ ?22 H0: ?12 > ?22 Ha: ?12 ≤ ?22 H0: ?12 ≠ ?22 Ha: ?12 = ?22 Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. We can conclude that the Fund B has a greater variance than Fund A.Do not reject H0. We cannot conclude that the Fund B has a greater variance than Fund A. Reject H0. We cannot conclude that the Fund B has a greater variance than Fund A.Do not reject H0. We can conclude that the Fund B has a greater variance than Fund A. Which fund is more risky? The more risky fund is .

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Investors commonly use the standard deviation of the monthly percentage return for a mutual fund as a measure of the risk for the fund; in such cases, a fund that has a larger standard deviation is considered more risky than a fund with a lower standard deviation. The standard deviation for a certain fund, referred to as Fund A, and the standard deviation for a second fund, Fund B, were recently reported to be 14.0% and 18.9%, respectively. Assume that each of these standard deviations is based on a sample of 60 months of returns. Do the sample results support the conclusion that the Fund B has a larger population variance than Fund A? (Assume that ? = 0.05.)

State the null and alternative hypotheses.

H₀: ?₁² ≤ ?₂²

H_a: ?₁² > ?₂²

H₀: ?₁² = ?₂²

H_a: ?₁² ≠ ?₂²

H₀: ?₁² > ?₂²

H_a: ?₁² ≤ ?₂²

H₀: ?₁² ≠ ?₂²

H_a: ?₁² = ?₂²

Find the value of the test statistic.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We can conclude that the Fund B has a greater variance than Fund A.Do not reject H₀. We cannot conclude that the Fund B has a greater variance than Fund A. Reject H₀. We cannot conclude that the Fund B has a greater variance than Fund A.Do not reject H₀. We can conclude that the Fund B has a greater variance than Fund A.

Which fund is more risky?

The more risky fund is .

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