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Given following problem:

enter image description here

I've solved this problem assuming two sided test and rejection region $R=\{|\bar{X_n}| > c\}$ but it seems to be incorrect because correct answer assumed (I've checked it) $R=\{\bar{X_n} > c\}$.

Is a two sided test (check null)? If so then why absolute value of mean is wrong for RR?

Thanks in advance.

Sharov
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In this case the parameter of the alternative is larger than the parameter for the null, so there is no need to do a two sided test. In other words, you can use your statistical power all on the right tail.

dmh
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  • Thank you very much! In other words, if I know location of alternative mean, there is no need in two sided test, meanwhile for tests like $\mu \neq 0$ I need two sided test, correct? – Sharov Sep 25 '20 at 17:52
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    Yes exactly, that's correct. – dmh Sep 25 '20 at 17:53