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Part CCSIR NET June 2023size-vs-power

Size vs power

Under H: X ~ p with p(x) = 1/20, and under K: X ~ q with q(x) = x/210, x ∈ {1, …, 20}. Define test functions if x ≤ 2 (else 0) and if x ≥ 19 (else 0). Which of the following statements are true?

  1. A.Size of the test is 0.1.✓
  2. B.Size of the test is 0.05.
  3. C.(Power of the test .✓
  4. D.(Power of the test Power of the test .✓

Solution

Sizes: P_H(X ≤ 2) = 2/20 = 0.1 and P_H(X ≥ 19) = 0.1. Powers: P_K(X ≥ 19) = 39/210 ≈ 0.186 and rejects where the likelihood ratio is largest — the Neyman–Pearson direction.

The trap it tests

What the inference means

p-values, size, power and error types say specific things. This was not one of them.

Drill statements like this

Related counterexample: A UMP test exists for every testing problem

More on this topic

From Hypothesis Testing › Neyman–Pearson lemma and UMP tests

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