FRM Part I · FRM Exam Part I · Hypothesis Testing
A risk manager tests whether a trading strategy's mean excess return is zero. In truth the strategy has a genuinely positive mean, but the test fails to reject H0: mean = 0. Which statement best describes this outcome?
This is a Type II error: the false null hypothesis was not rejected. Its probability, beta, equals one minus the power of the test. A Type I error would instead involve rejecting a true null hypothesis.
- AA Type I error, whose probability equals the significance level
- BA Type II error, whose probability equals 1 minus the power of the testCorrect
- CA Type I error, whose probability equals 1 minus the power
- DA correct decision, whose probability equals the confidence level
Explanation
Failing to reject a false null is a Type II error. Its probability is beta, and power equals 1 - beta. A Type I error would require rejecting a true null, with probability equal to the significance level.
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