A large-sample ?-level test of hypothesis for H0 : ? = ?0

Chapter 10, Problem 46E

(choose chapter or problem)

A large-sample \(\alpha\) -level test of hypothesis for \(H_{0}: \theta=\theta_{0}\) versus

\(H_{a}: \theta>\theta_{0}\) rejects the null hypothesis if

\(\frac{\widehat{\theta}-\theta_{0}}{\sigma_{\theta}}>Z_{\alpha}\)

Show that this is equivalent to rejecting \(H_{0}\) if  \(\theta_{0}\) is less than the large-sample \(100(1-\alpha) \%\) lower confidence bound for \(\theta\)

Equation Transcription:

Text Transcription:

\alpha

H_0: \theta=\theta_0

H_a: \theta>\theta_0

\frac\widehat\theta}-\theta_0 \sigma_\theta > Z_\alpha

H0

\theta_0

100(1-\alpha) \%

\theta

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