I think I'm confused with the concept of the P-Value. Take the hypothesis: Ho: u = 5 Ha: u != 5 And then take another hypothesis: Ho: u = 5 Ha: u > 5 I won't compute the p values, but it is easy to see that with the same statistic test, the p value for the first hypothesis will be twice that of the second, meaning that the statistic supports the second hypothesis much better than the first hypothesis. How can this be, especially when the second hypothesis is a sub case of the first hypothesis? What am I missing? Thanks.