Suppose that X1, , Xn form a random sample from the Poisson distribution with unknown mean , and suppose that it is desired to test the following hypotheses H0 1, H1 1 Suppose also that the sample size is n 10 At what levels of significance 0 in the interval 0 0 0 03 do there exist nonrandomized UMP tests

Question: Suppose that X1, . . . , Xn form a random sample from the Poisson distribution with unknown mean , and suppose that it is

Suppose that X1, . . . , Xn form a random sample from the Poisson with unknown mean λ, and suppose that it is desired to test the following hypotheses:
H0: λ ≥ 1,
H1: λ < 1.
Suppose also that the sample size is n = 10. At what levels of significance α0 in the interval 0 < α0 < 0.03 do there exist nonrandomized UMP tests?

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