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If I have to test a hypothesis like:

\begin{align} H_0:\mu\leq10\\H_1:\mu>10\\ Z_{1-p}=\dfrac{\bar{X}-\mu}{\sigma/\sqrt n} \end{align} From which I get p-value and I make a comment about whether it makes sense to reject $H_0$.

What happens for double sided tests? $\mu=10,\mu\neq10$.

Do I simply take $2\times p$ from the above and then make comments?

If yes, why are we doing that?

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    Yes. Ours is not to question why, ours is but to do or die.2012-12-14

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Now for a more serious answer.

You are correct that you take $2p$ where $p$ is the value from a table of normal distributions. This value represents the area under the curve of one tail of the normal distribution. With a double sided test, we need the area under the curve of both tails and so multiply by 2.

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    But why assume that the area of the tails will be the same?2012-12-14
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    @Inquest Because a normal distribution is symmetric about the y-axis. That is we can *show* that the tails are the same from the definition of the normal distribution; it's not an assumption.2012-12-14
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    If we were doing a two-tailed test on non-normal data (I've heard such a thing exists :P ), the calculation would be less simple, right?2012-12-14
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    @BenMillwood yes.2012-12-14
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    So, how would I test $\sigma=10, \sigma\neq 10$ using chi-squared. (Two sided of course).2012-12-14
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    I'm rusty on chi-squared tests, so I can't answer that without some review. I'd suggest starting with googling for "chi-squared two-sided test".2012-12-14
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    Update: you may want to ask this on our sister site [Stats.SE]. In particular, I found [this question](http://stats.stackexchange.com/questions/22347/chi-squared-always-a-one-sided-test) there.2012-12-14