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FRM Part I · FRM Exam Part I · Hypothesis Testing

Two trading desks have daily return samples. Desk A: n = 16, sample variance 9.0. Desk B: n = 21, sample variance 4.0. Testing H0: variances equal (two-sided) with the larger variance in the numerator, the F statistic is compared to a critical value F(15,20) = 2.20 at the relevant level. Which is correct?

With the larger variance in the numerator, F = 9.0/4.0 = 2.25 with 15 and 20 degrees of freedom. This exceeds the critical value of 2.20, so the hypothesis of equal variances is rejected.

  1. AF = 2.25 with 15 and 20 degrees of freedom; reject H0Correct
  2. BF = 2.25 with 20 and 15 degrees of freedom; reject H0
  3. CF = 0.44 with 15 and 20 degrees of freedom; reject H0
  4. DF = 2.25 with 15 and 20 degrees of freedom; fail to reject H0

Explanation

Desk A has the larger variance: F = 9/4 = 2.25, numerator df = 15, denominator df = 20. Since 2.25 > 2.20, reject H0. Inverting the ratio gives 0.44, which would not be compared to an upper critical value, and reversing df is wrong.

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