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FRM Part I · FRM Exam Part I · Hypothesis Testing

A risk analyst tests whether the variance of daily returns on a portfolio equals a hypothesized value, using a sample drawn from a normally distributed population. Which test statistic and distribution are appropriate?

The correct statistic is (n-1)s² divided by the hypothesized variance, which follows a chi-square distribution with n-1 degrees of freedom when the population is normal. The other statistics mix up the mean test, the F ratio, or the normal distribution.

  1. A(n-1)s²/σ0², which follows a chi-square distribution with n-1 degrees of freedomCorrect
  2. B(x̄-μ0)/(s/√n), which follows a chi-square distribution with n degrees of freedom
  3. Cs²/σ0², which follows an F distribution with n and n-1 degrees of freedom
  4. D(n-1)σ0²/s², which follows a standard normal distribution

Explanation

For a normal population, (n-1)s²/σ0² follows a chi-square distribution with n-1 degrees of freedom under the null that the variance is σ0². The other options use the wrong statistic, wrong distribution, or wrong degrees of freedom.

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