Solved: Let X1,X2, . . . ,Xn be a random sample of size n

Chapter 8, Problem 3E

(choose chapter or problem)

Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample of size \(n\) from the normal distribution \(N(\mu, 100)\).

(a) To test \(H_{0}: \mu=230\) against \(H_{1}: \mu>230\), what is the critical region specified by the likelihood ratio test criterion?

(b) Is this test uniformly most powerful?

(c) If a random sample of \(n=16\) yielded \(\bar{x}=232.6\), is \(H_{0}\) accepted at a significance level of \(\alpha=0.10\) ?

(d) What is the \(p\)-value of this test?

Equation Transcription:

.


Text Transcription:

X_1,X_2,,X_n

n

N(mu,100)

H_0:=230

H_1:>230  

n=16

Bar x=232.6

H_0 =0.10  

p

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