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FRM Part I · FRM Exam Part I · Hypothesis Testing

A normally distributed return series has 31 observations and a sample variance of 0.0050. Which expression gives the 95% confidence interval for the population variance, where chi-square values have 30 degrees of freedom?

The confidence interval for variance runs from (n-1)s^2 divided by the upper 2.5% chi-square point to (n-1)s^2 divided by the lower 2.5% point, using 30 degrees of freedom. The larger critical value gives the lower bound.

  1. A[30 x 0.0050 / chi2 upper 2.5% point, 30 x 0.0050 / chi2 lower 2.5% point]Correct
  2. B[30 x 0.0050 / chi2 lower 2.5% point, 30 x 0.0050 / chi2 upper 2.5% point]
  3. C[31 x 0.0050 / chi2 upper 2.5% point, 31 x 0.0050 / chi2 lower 2.5% point]
  4. D[0.0050 +/- 1.96 x 0.0050 / sqrt(31)]

Explanation

The interval is (n-1)s^2 divided by the upper critical value for the lower bound, and by the lower critical value for the upper bound. Swapping them inverts the interval, using n is wrong, and the normal-based form is for a mean.

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