Suppose that we wish to test versus where the population
Chapter 9, Problem 171MEE(choose chapter or problem)
Suppose that we wish to test \(H_{0}: \mu=\mu_{0}\) versus \(H_{1}: \mu \neq \mu_{0}\) where the population is normal with known \(\sigma\). Let \(0<\boldsymbol{\epsilon}<\alpha\), and define the critical region so that we will reject \(H_{0}\) if \(z_{0}>z_{\epsilon}\) or if
\(z_{0}<-z_{\alpha-\epsilon}\), where \(z_{0}\) is the value of the usual test statistic for these hypotheses.
(a) Show that the probability of type I error for this test is \(\alpha\).
(b) Suppose that the true mean is \(\mu_{1}=\mu_{0}+\delta\). Derive an expression for \(\beta\) for the above test.
Equation Transcription:
Text Transcription:
H_0: \mu=\mu_0
H_1: \mu \neq \mu_0
\sigma
0<\boldsymbol \epsilon<\alpha
H_0
z_0>z_\epsilon
z_0<-z_\alpha-\epsilon
Z_0
\alpha
\mu_1=\mu_0+\delta
\beta
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