Solution Found!
Let X1,X2, . . . ,X10 be a random sample of size 10 from a
Chapter 8, Problem 7E(choose chapter or problem)
Let\(X_{1}, X_{2}, \ldots, X_{10}\) be a random sample of size 10 from a Poisson distribution with mean \(\mu\).
(a) Show that a uniformly most powerful critical region for testing \(H_{0}: \mu=0.5\) against \(H_{1}: \mu>0.5\) can be defined with the use of the statistic \(\sum_{i=1}^{10} X_{i}\).
(b) What is a uniformly most powerful critical region of size \(\alpha=0.068\) ? Recall that \(\sum_{i=1}^{10} X_{i}\) has a Poisson distribution with mean \(10 \mu\).
(c) Sketch the power function of this test.
Equation Transcription:
Text Transcription:
X_1,X_2,,X_10
H_0:=0.5
H_1:>0.5
sum_i=1^10 X_i
alpha =0.068
sum_i=1^10 X_i
10 mu
Questions & Answers
QUESTION:
Let\(X_{1}, X_{2}, \ldots, X_{10}\) be a random sample of size 10 from a Poisson distribution with mean \(\mu\).
(a) Show that a uniformly most powerful critical region for testing \(H_{0}: \mu=0.5\) against \(H_{1}: \mu>0.5\) can be defined with the use of the statistic \(\sum_{i=1}^{10} X_{i}\).
(b) What is a uniformly most powerful critical region of size \(\alpha=0.068\) ? Recall that \(\sum_{i=1}^{10} X_{i}\) has a Poisson distribution with mean \(10 \mu\).
(c) Sketch the power function of this test.
Equation Transcription:
Text Transcription:
X_1,X_2,,X_10
H_0:=0.5
H_1:>0.5
sum_i=1^10 X_i
alpha =0.068
sum_i=1^10 X_i
10 mu
ANSWER:Step 1 of 4
Given:
The size of the sample is 
The variables 
