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FRM Part I · FRM Exam Part I · Hypothesis Testing

A trader claims the annual volatility of a strategy is 20% (σ0² = 0.04). From 25 annual observations, the sample standard deviation is 16% (s² = 0.0256). Assuming normally distributed returns, a two-sided chi-square test at the 5% level has critical values 12.401 and 39.364 for 24 degrees of freedom. Which conclusion is correct?

The chi-square statistic is 24 × 0.0256 / 0.04 = 15.36. It falls between the two-sided critical values 12.401 and 39.364, so the null hypothesis of 20% volatility cannot be rejected at the 5% level.

  1. AStatistic is 15.36; it lies between the critical values, so do not reject the 20% volatility claimCorrect
  2. BStatistic is 15.36; it is below the degrees of freedom of 24, so reject the claim
  3. CStatistic is 38.40; it is below 39.364, so reject the claim
  4. DStatistic is 0.64; it is below 12.401, so reject the claim

Explanation

Statistic = 24 × 0.0256 / 0.04 = 15.36. This lies between 12.401 and 39.364, so H0 is not rejected. Comparing to the degrees of freedom is not the decision rule. The other options use an incorrect statistic.

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