Let X 1 ,X 2 , , X 10 denote a random sample of size 10 from a Poisson distribution with mean Show that the critical region C defined by 10 1 x i 3 is a best critical region for testing H 0 0 1 against H 1 0 5 Determine, for this test, the significance level and the power at 0 5

Question: Let X 1 ,X 2 , . . . , X 10 denote a random sample of size 10 from a Poisson distribution with mean

Let X₁,X₂, . . . , X₁₀ denote a random sample of size 10 from a Poisson distribution with mean θ. Show that the critical region C defined by Σ¹⁰₁ x_i ≥ 3 is a best critical region for testing H₀ : θ = 0.1 against H₁ : θ = 0.5. Determine, for this test, the significance level α and the power at θ = 0.5.

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