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FRM Part I · FRM Exam Part I · Hypothesis Testing

A analyst runs a two-sided test of H0: mu = 0 on a strategy's monthly excess return and obtains a 95% confidence interval for mu of (0.10%, 1.30%). Which conclusion is consistent with this interval?

Because zero lies outside the 95% confidence interval, the two-sided test rejects the null at 5%. A 90% interval is narrower and is contained within the 95% interval, so it also excludes zero, and the null is rejected at 10% too.

  1. AReject H0 at the 5% level, and also reject at the 10% levelCorrect
  2. BFail to reject H0 at the 5% level, but reject at the 10% level
  3. CFail to reject H0 at the 5% level because the interval is wide
  4. DReject H0 at the 5% level, but nothing can be said at the 10% level

Explanation

Zero lies outside the 95% interval, so the two-sided test rejects at 5%. A 90% interval is narrower and nested inside the 95% interval, so it also excludes zero, meaning rejection at 10% as well. Width of the interval is irrelevant to the decision rule.

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