### CFA Practice Question

An analyst is researching two mutual funds ABC and DEF. The analyst has a sample of 24 monthly returns of ABC and 30 monthly returns of DEF. The sample standard deviation for ABC is 1.1768% and for DEF is 1.7154%.

F(29, 23, 0.05) = 1.967
F(29, 23, 0.025) = 2.247

You want to test the Null hypothesis that the two variances are equal at 5% level of significance. What is the F test statistic value, the threshold level for rejection of the Null, and the decision?
A. 1.4577, 1.967, and fail to reject respectively.
B. 2.1248, 2.247, and fail to reject respectively.
C. 2.1248, 1.967, and reject respectively.
Explanation: Remember that we are testing whether the variances are unequal (two-tailed test). However, we eliminate the left tail simply by choosing to put the larger variance in the numerator. So the remaining (right) tail should be the only region of rejection (even though the null says that the variances are equal).

User Comment
andrewmorgan how do they get 2.1248? (1.7154/1.1768)^2.
shawnpope yes andrew, the F-test statistic is the ratio of the larger variance over the smaller variance. In this case that is
(1.7154^2/1.1768^2) = 2.1248

Use the F value (30-1, 24-1, two-tailed test = 0.025) = 2.247

2.1248<2.247 fail to reject
sunday128 You can actually pick the answer without even doing the calculations.

1) They are asking test of equality which means it is a 2 tail test.
2) Given 95% level of confidence, alpha = 0.05 and 2 tails means 0.025.
3) There is only one answer for a 2 tail test, thus B.