Question: Let X1 X2 X8 be a random sample

Let X1, X2, ... , X8 be a random sample of size n = 8 from a Poisson distribution with mean λ. Reject the simple null hypothesis H0: λ = 0.5, and accept H1: λ > 0.5, if the observed sum 8i=1 xi ≥ 8.
(a) Compute the significance level α of the test.
(b) Find the power function K(λ) of the test as a sum of Poisson probabilities.
(c) Using Table III in Appendix B, determine K(0.75), K(1), and K(1.25).

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