NETMaths
Part BCSIR NET December 2023direction-of-rejection

Direction of rejection

Let be a random sample from the gamma density f(x| for unknown. Let and be the UMP test of size 0.05 for against . With the th quantile of , the test rejects iff

  1. A.T ≥ ½
  2. B.T ≤ ½
  3. C.T ≥ ½
  4. D.T ≤ ½

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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

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From Hypothesis TestingNeyman–Pearson lemma and UMP tests

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