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
Part BCSIR NET December 2023direction-of-rejection
Direction of rejection
Related counterexample: A UMP test exists for every testing problem
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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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