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FRM Part I · FRM Exam Part I · Hypothesis Testing

A bank's model validation team tests H0: the model is adequate, against H1: the model is inadequate. They fail to reject H0, but the model is in fact inadequate. Which statement best describes this outcome, and what happens to it if the significance level is raised from 5% to 10%, holding sample size and true parameters fixed?

This is a Type II error, since a false null was not rejected. Raising the significance level from 5% to 10% enlarges the rejection region, which lowers the probability of a Type II error and raises power, while increasing the Type I error probability.

  1. AType I error; its probability would rise
  2. BType II error; its probability would fallCorrect
  3. CType II error; its probability would rise
  4. DType I error; its probability would fall

Explanation

Failing to reject a false null is a Type II error. Raising the significance level widens the rejection region, making rejection more likely when H0 is false, so beta falls and power rises (at the cost of a higher Type I error rate).

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