How to choose the original hypothesis in statistics

This question is a confusing one for every student who learns this part.

Set the original hypothesis for H0, alternative hypothesis for H1, the confidence level of 95%

H0 and H1 from the logic of the original hypothesis was two choose one, either one or the other, for the original hypothesis of the results of the test logically there are only two, either the right, or the wrong, if H0 is right, then H1 must be wrong, if H0 is wrong, then H1 must be right, so that If H0 is wrong, then H1 must be right, and so on, whichever one is chosen as the original hypothesis should lead to the same result. But in fact, it makes a difference which one is chosen as the original hypothesis, so where does the problem lie?

In fact, the problem lies in the results of hypothesis testing, statistics used in the hypothesis testing method, for the original hypothesis to get the conclusion is not "right" and "wrong" two results, but "rejected What's the difference between "right" and "wrong" for the original hypothesis, but "reject" and "accept"?

It is important to note that when doing hypothesis testing, a confidence level is set, and when we "reject" the original hypothesis, we are in fact only saying that "we are 95% sure" that the original hypothesis is wrong, that is to say, it is still possible to be right, in other words, it is not the case that the original hypothesis is wrong. In other words, we cannot logically reject the original hypothesis!

Then we come back to "accepting" the original hypothesis, and this word "accepting" has hurt almost all of our students, but in fact the exact word should be "not rejecting" the original hypothesis. For example, the original hypothesis H0 is: expectation = 2, if "reject" H0, then means we have 95% certainty that H0 is wrong, but when we so-called "accept" H0, we do not have 95% certainty that the expectation is equal to 2, in fact, we have no certainty at all. 2, in fact, we do not have any certainty, we just use the existing sample data can not be denied that it is 2 only, it may be 2.1, 2.11,1.95 ....... And so on and so forth.

In summary, we note two things: first, our "rejection" and "acceptance" of the original hypothesis, not logical right or wrong; second, our "rejection" of the original hypothesis and "acceptance" of the original hypothesis, not logical right or wrong; second, our "rejection" of the original hypothesis and "acceptance" of the original hypothesis, not logical right or wrong. The second is that our "rejection" of the original hypothesis and our "acceptance" of the original hypothesis are completely unequal. When we reject the original hypothesis, we are 95% sure, but when we accept the original hypothesis, we are not sure at all. From this we can see that when we choose the original hypothesis, we should choose the side in which we are more certain to reject it.

A more detailed discussion of this issue involves the length of the confidence interval, the need to draw a diagram, it is difficult to get here, find your own information to see it.