FRM Part I · FRM Exam Part I · Hypothesis Testing
Daily excess returns of a strategy have a known population standard deviation of 3.0%. A sample of 100 days gives a mean excess return of 0.9%. Testing H0: mu = 0 against H1: mu > 0 at the 1% significance level (critical z = 2.326), which conclusion is correct?
The z-statistic is 3.00, since the standard error is 3.0 divided by 10, or 0.30, and the mean is 0.9. This exceeds the one-sided 1% critical value of 2.326, so the null hypothesis of zero mean excess return is rejected.
- Az = 3.00; reject H0Correct
- Bz = 0.30; do not reject H0
- Cz = 30.0; reject H0
- Dz = 3.00; do not reject H0 at the 1% level
Explanation
The standard error is 3.0/sqrt(100) = 0.30. The z-statistic is 0.9/0.30 = 3.00, which exceeds 2.326, so H0 is rejected. The value 0.30 forgets to divide the mean by the standard error. The value 30 divides by 3.0/100.
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