Show that [ begin{aligned} & P_{H_{1}}left(frac{bar{X}-mu_{0}}{frac{S}{sqrt{n}}} geq t_{n-1,1-alpha / 2} ight)+P_{H_{1}}left(frac{bar{X}-mu_{0}}{frac{S}{sqrt{n}}} Let X1, ..., X, be i.i.d.
Question:
Show that
\[
\begin{aligned}
& P_{H_{1}}\left(\frac{\bar{X}-\mu_{0}}{\frac{S}{\sqrt{n}}} \geq t_{n-1,1-\alpha / 2}\right)+P_{H_{1}}\left(\frac{\bar{X}-\mu_{0}}{\frac{S}{\sqrt{n}}}<-t_{n-1,1-\alpha / 2}\right) \\
= & P\left(t_{n-1, \gamma} \geq t_{n-1,1-\alpha / 2}\right)+P\left(t_{n-1, \gamma}<-t_{n-1,1-\alpha / 2}\right) .
\end{aligned}
\]
The right-hand side is the final expression for the power of the t-test in Section 4.4 .
Data from Section 4.4
............
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Related Book For
Design And Analysis Of Experiments And Observational Studies Using R
ISBN: 9780367456856
1st Edition
Authors: Nathan Taback
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