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 α = 0.05.)

State the null and alternative hypotheses.

H₀: σ₁² > σ₂²

H_a: σ₁² ≤ σ₂²

H₀: σ₁² = σ₂²

H_a: σ₁² ≠ σ₂²

H₀: σ₁² ≤ σ₂²

H_a: σ₁² > σ₂²

H₀: σ₁² ≠ σ₂²

H_a: 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 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  ---Select--- Fund A or Fund B .

Answer 1

Answer:

Given,

Here Fund B has larger population variance than Fund A

Ho : <=

Ha : >

Consider,

F statistic = s2^2 / s1^2

substitute values

= 18.9^2 / 14^2

= 1.8225

Sample n = 60

degree of freedom = n - 1 = 60 - 1 = 59

alpha = 0.05

P value = 0.011346 [since from f table]

= 0.0113

Here we observe that, p value < alpha, so we reject Ho.

So there is sufficient evidence i.e., Fund B has greater variance than A.

So it is more risky.