# p value : Confusion in basics [closed]

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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## closed as off-topic by Austin Mohr, Sami Ben Romdhane, TooTone, Shuchang, 6005Feb 28 '14 at 1:14

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Yes. Ours is not to question why, ours is but to do or die. –  Code-Guru Dec 14 '12 at 2:26

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.
So, how would I test $\sigma=10, \sigma\neq 10$ using chi-squared. (Two sided of course). –  Inquest Dec 14 '12 at 3:18