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FRM Part I · FRM Exam Part I · Hypothesis Testing

An analyst tests whether a mean return differs from zero. The 95% confidence interval for the mean is 0.30% to 2.10%. Which conclusion is correct for a two-sided test at the 5% significance level of H0: mean = 0?

Reject the null hypothesis. A 95% confidence interval corresponds to a two-sided 5% test, and any hypothesized value outside the interval is rejected. Zero lies below the lower bound of 0.30%, so the mean is statistically different from zero.

  1. AReject H0, because zero lies outside the intervalCorrect
  2. BFail to reject H0, because the interval is narrow
  3. CFail to reject H0, because the sample mean is positive
  4. DReject H0 only if the interval is also centered on zero

Explanation

A two-sided test at 5% rejects any hypothesized value lying outside the 95% confidence interval. Zero is below 0.30%, so it falls outside and H0 is rejected. Interval width and the sign of the mean do not determine the decision.

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