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If we want to test the hypothesis $H_0$: $\mu = 0$, where $H_a$: $\mu \neq 0$. Then the t statistic is $t=\bar{y}/(s/\sqrt{n})$ and 95% confidence interval is $\bar{y} \pm t_{.975}s/\sqrt{n}$ by t-test. If the sample mean $\bar{y} > 0$, why the rejection region is $t>t_{.975}$ instead of $t<-t_{.975}$?

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  • $\begingroup$ I am not sure I understand your question - the rejection region for a two-tailed test will be $|t| > t_{0.975}$ (i.e. $t>t_{0.975}$ or $t<-t_{0.975}$) regardless of the value of $\bar{y}$? $\endgroup$
    – B.Liu
    Feb 19, 2022 at 15:50

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