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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

Which statement about the critical region of a most powerful test of a simple null hypothesis against a simple alternative, as given by the Neyman-Pearson lemma, is correct?

The most powerful test of a given size rejects the null hypothesis when the ratio of the alternative likelihood to the null likelihood is at least a constant, with that constant set to achieve the required significance level.

  1. AIt consists of the values of the data for which the likelihood ratio L(H0)/L(H1) is at least as large as a constant
  2. BIt consists of the values of the data for which the likelihood ratio L(H1)/L(H0) is at least as large as a constant chosen to give the required sizeCorrect
  3. CIt is always the upper tail of the sample mean
  4. DIt is chosen to make the Type II error probability equal to the Type I error probability
  5. It is chosen to maximise the p-value for the observed data

Explanation

The Neyman-Pearson lemma says the most powerful test of given size rejects H0 when L(H1)/L(H0) ≥ k, with k fixed by the size. It is not always an upper tail of the mean; the region depends on the likelihoods. Equalising error probabilities is not the criterion.

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