Question

Let X1, X2, X3, X4 be a random sample from a Poisson distribution with unknown mean λ > 0. For testing the hypothesis
H0 : λ = 1 against H1 : λ = 1.5,
let β denote the power of the test that rejects H0 if and only if $∑_{i=1}^4 𝑋_𝑖 ≥ 5$. Then which one of the following statements is true ?

• A. β > 0.80
• B. 0.75 < β ≤ 0.80
• C. 0.70 < β ≤ 0.75
• D. 0.65 < β ≤ 0.70

Answer 1

Answer: (C)

0.70 < β ≤ 0.75

Answer 2

The correct option is (C) : 0.70 < β ≤ 0.75.