9. Let X₁,..., X10 denote a random sample of size 10 of a Poisson distribution with mean 0. Show that the test that rejects H₁ : 0 = 0.1 in favour of H₁ : 0 = 0.5 if Σ1₁ X; ≥ 3 is most powerful. Determine, for this test, the significance level a and the power at 0 = 0.5.

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Q: 12

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