Question 1086019: A significance test is performed and p = .20. Why can’t the experimenter claim that the probability that the null hypothesis is true is .20?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Quick answer: The null hypothesis deals with parameters, not statistics, and the parameter is either true or false after the test has been done. We don't know which one it is, but there is only one possibility, not a probability any more.
The null hypothesis is set and so should alpha be defined at the outset, before the experiment done and the data are collected. It should be clearly stated a priori that if the likelihood of the result being what it is or one more extreme is greater than the test statistic, then the null hypothesis will be rejected.
The test is done with a given null hypothesis, and the probability of getting the result one got or one more extreme, given that the null hypothesis is true, is 0.20. That is what the 0.20 is about, not the probability that the null hypothesis is true. After the fact, the null hypothesis is either true or false, a 100%-0% situation, and no in-between. That is why confidence intervals are constructed and not probability intervals.
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