Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter B.2, Problem 16AYU
Investment Risk Investors not only desire a high return on their money, but they would also like the rate of return to be stable from year to year. An investment manager invests with the goal of reducing volatility (year-to-year fluctuations in the rate of return). The following data represent the rate of return (in percent) for his mutual fund for the past 12 years.
- (a) Verify that the data are
normally distributed by constructing a normal probability plot. - (b) Determine the sample standard deviation.
- (c) Construct a 95% confidence interval for the population standard deviation of the rate of return.
- (d) The investment manager wants to have a population standard deviation for the rate of return below 6%. Does the confidence interval validate this desire?
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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 15.0% and 19.2%, 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.)
test statistic is 1.6384 p-value = 0.0301
State your conclusion.
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.
Do not reject H0. We cannot conclude that the Fund B has a greater variance than Fund A.…
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 15.0% and 19.2%, 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: σ12 > σ22
Ha: σ12 ≤ σ22
H0: σ12 ≤ σ22
Ha: σ12 > σ22
H0: σ12 = σ22
Ha: σ12 ≠ σ22
H0: σ12 ≠ σ22
Ha: σ12 = σ22
Find the value of the test statistic.
( )
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject…
Chapter B.2 Solutions
Fundamentals of Statistics (5th Edition)
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