A large-sample ?-level test of hypothesis for H0 : ? = ?0
Chapter 10, Problem 48E(choose chapter or problem)
A large-sample -level test of hypothesis for \(H_{0}: \Theta=\Theta_{0}\) versus \(H_{a}: \Theta<\Theta_{0}\) rejects the null hypothesis if
\(\frac{\overline{\tilde{\Theta}}-\Theta_{0}}{\sigma_{\bar{\theta}}}<-z_{\alpha}\)
Show that this is equivalent to rejecting \(H_{0}) if \(\Theta_{0}\) is greater than the large-sample \(100(1-\alpha) \%\) upper confidence bound for \(\Theta)\.
Equation transcription:
Text transcription:
H_{0}: Theta=\Theta{0}
H_{a}: Theta<\Theta{0}
frac{\overline{\tilde{\Theta}}-\Theta{0}}{\sigma{\bar{\theta}}}<-z{\alpha}
H_{0}
Theta{0}
100(1-\alpha) \%
Theta
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