Standard deviation of returns is often used as a measure of a mutual fund’s vola

Question

Standard deviation of returns is often used as a measure of a mutual fund’s volatility (risk). A larger standard deviation of returns is an indication of higher risk. According to Morningstar.com (June 17, 2010), the American Century Equity Income Institutional Fund, a large cap fund, has a standard deviation of returns equal to 14.98 percent. Morningstar.com also reported that the Fidelity Small Cap Discovery Fund has a standard deviation of returns equal to 21.78 percent. Each standard deviation was computed using a sample of size 36. Perform a hypothesis test to determine if the variance of returns for the Fidelity Small Cap Discovery Fund is larger than the variance of returns for the American Century Equity Income Institutional Fund. Perform the test at the .01 level of significance, and assume normality.

Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Calculate the critical value. (Round your answer to 2 decimal places.)

Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Calculate the critical value. (Round your answer to 2 decimal places.)

Explanation / Answer

Null, Ho: ^2 > ^2
Alternate, H1: ^2 < ^2
Test Statistic
Sample 1
s1^2= = 21.78^2 = 474.3684, n1 =36
Sample 2
s2^2 =14.98^2 = 224.4004, n2 =36
Fo = 474.3684/224.4004 = 2.11
| Fo | =2.11
Critical Value
The Value of |F | at LOS 0.05 with d.f F(n1-1,n2-1)=F(35,35) is 1.757
We got |Fo| =2.114 & | F | =1.757
Make Decision
Hence Value of | Fo | > | F | and Here we Reject Ho

[ANSWERS]
1. test statistic. = 2.11
2. Critical Value: 1.757

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