FRM Part I · FRM Exam Part I · Hypothesis Testing
Holding the sample size and true parameter value fixed, a researcher lowers the significance level of a two-sided z-test from 5% to 1%. Which is the effect on the test?
Type I error probability falls and power falls. A stricter 1% level widens the non-rejection region, so the test rejects less often, including when the null is false, which raises the Type II error probability and lowers power.
- AProbability of Type I error falls and power fallsCorrect
- BProbability of Type I error falls and power rises
- CProbability of Type I error rises and power falls
- DProbability of Type II error falls and power rises
Explanation
A lower significance level means a smaller Type I error probability and a larger critical value, making rejection harder. With the sample size fixed, the Type II error probability rises, so power falls. The trade-off is why alpha cannot be cut without cost.
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