FRM Part I · FRM Exam Part I · Hypothesis Testing
Two independent samples of 36 monthly returns each are drawn from funds A and B. Fund A has a mean of 7.2% and standard deviation of 4.0%; fund B has a mean of 5.6% and standard deviation of 3.0%. Using the unpooled standard error, what is the test statistic for H0: mu_A - mu_B = 0?
The test statistic is 1.92. The standard error of the difference is the square root of 16/36 plus 9/36, which is 0.8333, and the difference in sample means is 1.6 percentage points, so 1.6 divided by 0.8333 equals 1.92.
- A1.92Correct
- B1.37
- C2.72
- D0.32
Explanation
The standard error is sqrt(16/36 + 9/36) = sqrt(25/36) = 0.8333. The difference is 1.6, so the statistic is 1.6/0.8333 = 1.92. Adding the standard deviations instead of variances gives 1.37. Dividing by 5 (the root of summed variances without dividing by n) gives 0.32.
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