Let x1, x2, x3 be a random sample of size 3 from a Poisson distribution with mean lambda 0. To test H0 : lambda = 1/8 versus H1 : lambda = 1, reject H0 when sumi=1^3xi 1. The power of the test is approximately (given e^-3 = 0.04978)

Q34Section I (Objective (Q1–Q80))34 of 80

Statistical Inference — power of a test for Poisson mean

Let $\{x_1, x_2, x_3\}$ be a random sample of size 3 from a Poisson distribution with mean $\lambda > 0$ . To test $H_0 : \lambda = \frac{1}{8}$ versus $H_1 : \lambda = 1$ , reject $H_0$ when $\sum_{i=1}^{3}x_i > 1$ . The power of the test is approximately (given $e^{-3} = 0.04978$ )

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