I have learned that a p-value that is less than alpha means you reject the null hypothesis. But this seems to only make sense in the case of lower tail tests. What do you do for upper tail tests?
Solved – In hypothesis testing, does a p-value less than alpha always mean you reject NH
hypothesis testingp-value
Best Answer
The p-value applies to upper, lower, and double tailed tests. It is the probability that the test statistic would be at least as contradictory to your null hypothesis as you currently observe assuming your null hypothesis is true. So, for upper tail tests, you are comparing $H_o: a = b$ vs. $H_a: a>b$, in this case, the p-value is the probability that the test statistic would be at least as high as you observe, assuming a=b, so you calculate 1 - CDF of the test statistic under the null hypothesis and see if it meets your type I error rate requirement.