Let X1,X2, . . . ,X8 be a random sample of size n = 8 from
Chapter 8, Problem 10E(choose chapter or problem)
Let \(X_{1}, X_{2}, \ldots, X_{8}\) be a random sample of size \(n=8\) from a Poisson distribution with mean \(\lambda\). Reject the simple null hypothesis \(H_{0}: \lambda=0.5\), and accept \(H_{1}:\) \(\lambda>0.5\), if the observed \(\operatorname{sum} \sum_{i=1}^{8} x_{i} \geq 8\).
(a) Compute the significance level \(\alpha\) of the test.
(b) Find the power function \(K(\lambda)\) of the test as a sum of Poisson probabilities.
(c) Using Table III in Appendix B, determine \(K(0.75)\), \(K(1)\), and \(K(1.25)\).
Equation Transcription:
,
Text Transcription:
X_1,X_2,…,X_8
n=8
H_0:=0.5
H_1: >0.5
sum_i=1^8 x_i > or = 8
K(labda)
K(0.75), K(1)
K(1.25)
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