FRM Part I · FRM Exam Part I · Hypothesis Testing
A fund manager claims the standard deviation of monthly returns is 4.0%. A sample of 21 monthly returns gives a sample standard deviation of 5.0%. Assuming normality, what is the chi-square test statistic for H0: σ² = 16 (in %²)?
The test statistic is 31.25. It equals 20 degrees of freedom times the sample variance of 25 divided by the hypothesized variance of 16. Using 21 instead of 20 would wrongly give 32.81.
- A31.25Correct
- B25.00
- C20.00
- D32.81
Explanation
Statistic = (n-1)s²/σ0² = 20 × 25 / 16 = 31.25, with 20 degrees of freedom. Using n instead of n-1 gives 32.81; using the ratio of standard deviations inverted gives 20×16/25 = 12.8, not listed; 25.00 omits the factor properly.
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