# Math Help - Issues with understanding P-values

1. ## Issues with understanding P-values

After doing a couple of questions I realised that I have not fully grasped the concept of understanding the rejection region step of small-sample inferences aswell as Large-sample tests.

the P-value method is quite confusing, perticularly when the two-sided tailed tests are put into play. My knowledge of critical value is also effected by it. I know about alpha and the significance level used for the test. Its basically the comparing the test calculated values with the alpha for determining the rejection region, that is confusing me.

Here are some questions that are using the P-values in different ways which is the primary root of my problem

EDIT:

I can't post the questions since they are lengthy and I don't have a scanner at the moment but here is the solutions which show how the p-value is taken.

solution manuel:
:

If it comes to requiring the questions, I would post them sooner or later.

2. I'm not sure what the question is here.
BUT the p-value is determined by the ALTERNATIVE hypothesis and the test stat.

In testing a mean with say > in the alternative and test stat say 2.
Then the p-value is $P(Z>2)$ assuming we know sigma or are approximating with the central limit theorem

IF you have a two sided test, say $H_a:\mu\ne 1001$ and a test stat of 2 again then the p-value is $2P(Z>2)$

Basically the p-value is the probability of being WORSE off than the test stat in any setting.