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matheagle · #8 June 30th, 2009, 06:18 PM

Quote:

Originally Posted by chrissy72

I do.
For means I have (for known variance) $H_{0}: \mu=\mu_{0}$ $H_{1}: \mu>\mu_{0}$

$z \ge z_{\alpha}$ OR $\bar{x} \ge \mu_{0}+z_{\alpha}\sigma/\sqrt{n}$

For unknown variance

$t \ge t_{\alpha}(n-1)$ OR $\bar{x} \ge \mu_{0}+t_{\alpha}(n-1)s/\sqrt{n}$

The second one is exactly this...

$\bar{x} \ge \mu_{0}+t_{\alpha}(n-1)s/\sqrt{n}$

is the same as ${\bar{x}-\mu_{0}\over s/\sqrt n}>t_{\alpha}(n-1)$

WHERE the test stat is ${\bar{x}-\mu_{0}\over s/\sqrt n}$

and the rejection region is $(t_{\alpha}(n-1), \infty)$

and $\mu_{0}=0$ since under the null hypothesis you ARE assumng that $\mu$ is 0.

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chrissy72
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