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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 φ(x)=1\varphi(x) = 1 if x ≤ 2 (else 0) and ψ(x)=1\psi(x) = 1 if x ≥ 19 (else 0). Which of the following statements are true?

  1. A.Size of the test φ\varphi is 0.1.✓ Correct
  2. B.Size of the test ψ\psi is 0.05.
  3. C.(Power of the test ψ)>0.05\psi) > 0.05.✓ Correct
  4. D.(Power of the test ψ)>(\psi) > (Power of the test φ)\varphi).✓ Correct

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests what the inference means.

See pricing

50 are analysed free — try those first.

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

The chapter behind this: Neyman–Pearson and UMP tests — free to read

From Hypothesis Testing › Neyman–Pearson lemma and UMP tests

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