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FRM Part I · FRM Exam Part I · Hypothesis Testing

Which statement about chi-square tests of a single variance and F-tests for equality of two variances is correct?

Both the chi-square test for one variance and the F-test for two variances assume normally distributed populations and are sensitive to departures from normality, even in large samples. The F statistic is never negative, and the standard F-test assumes independent samples.

  1. ABoth rely on normally distributed data and can be unreliable if the population is substantially non-normal, even with large samplesCorrect
  2. BBoth are robust to non-normality because the central limit theorem applies to sample variances
  3. CThe F statistic can be negative when the sample variance in the numerator is smaller than in the denominator
  4. DThe F-test for two variances requires the two samples to be paired and dependent

Explanation

Variance tests depend on normality of the underlying data; unlike tests on means, the central limit theorem does not rescue them. The F statistic is a ratio of nonnegative variances and cannot be negative. The standard F-test assumes independent samples, not paired ones.

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