2 Suppose that you want to perform a hypothesis test regardi

2. Suppose that you want to perform a hypothesis test regarding a population mean and the evidence does not warrant the rejection of the null hypothesis. When formulating the conclusion to the test, why is the phrase, \"fail to reject the null hypothesis\" more accurate that the phrase \"accept the null hypothesis\"?

Solution

We never accept null hypothesis, because we never actually prove it. we always assume it true and try to disprove it. When sample is unable to disprove it, we conclude that it is plausible that the null is true, but there can be infinite number of test variables that would be \"plausible\". \"Fail to reject\" helps us identify that null may still not be true.