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FRM Part I · FRM Exam Part I · Hypothesis Testing

A 95% confidence interval for a portfolio's mean annual excess return is computed as 2.0% to 8.0% from a large sample. A risk manager uses this interval to test H0: mean = 0 against a two-sided alternative at the 5% significance level. Which conclusion is correct?

Reject the null hypothesis. A two-sided 5% test rejects any hypothesized mean that falls outside the 95% confidence interval, and zero lies below the lower bound of 2.0%. Interval width or midpoint alone does not decide the test.

  1. AReject H0, because zero lies outside the intervalCorrect
  2. BFail to reject H0, because the interval is wide
  3. CFail to reject H0, because the interval midpoint of 5.0% exceeds zero
  4. DReject H0 only if the test is one-sided

Explanation

A two-sided test at 5% rejects any hypothesized value outside the 95% confidence interval. Zero is below 2.0%, so it lies outside and H0 is rejected. Interval width does not determine the decision, and the midpoint being positive is the sample estimate, not the test criterion.

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