FRM Part I · FRM Exam Part I · Hypothesis Testing
A risk manager tests H0: sigma^2 = 4 against H1: sigma^2 > 4 for daily P&L (normal) using 21 observations. The sample variance is 6.5. The chi-square critical value at 5% significance with 20 degrees of freedom (upper tail) is 31.41. What is the correct conclusion?
The statistic is 20 x 6.5 / 4 = 32.5, which is above the 5% upper-tail critical value of 31.41, so the null that variance equals 4 is rejected in favor of variance being greater than 4.
- ATest statistic 32.5 exceeds 31.41; reject H0Correct
- BTest statistic 32.5 exceeds 31.41; fail to reject H0
- CTest statistic 31.0 is below 31.41; fail to reject H0
- DTest statistic 34.1 exceeds 31.41; reject H0
Explanation
Statistic = 20 x 6.5 / 4 = 32.5. This exceeds 31.41, so H0 is rejected in this upper-tail test. The other options either miscompute the statistic or draw the wrong conclusion.
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