The given hypothesis is tested with the help of the sample data. A simple random sample has the full freedom of giving any value to its statistics. The sample is not aware of our plans, and we choose our hypothesis on the basis of the sample statistics. If the sample does not support the null hypothesis, we reject it on the probability basis and accept the alternative hypothesis. If the sample does not oppose the hypothesis, the hypothesis is accepted.
However, here ‘accept’ does not mean the acceptance of the null hypothesis, it only means that the sample has not strongly opposed it. “Not opposed” does not mean that the sample has strongly supported the hypothesis. The support of the sample in favor of the hypothesis cannot be established. When the hypothesis is rejected, it is rejected with a high probability.
Thus the rejection of : is a strong decision and it leads us to the acceptance of . But the acceptance of is not like the acceptance of . The acceptance of the null hypothesis does not give us a certain strong decision; it is a situation which may require some further investigation. At this stage, many factors must be taken into account. The sample size and certain other features not yet discussed help us to investigate the null hypothesis more before it is finally accepted. Thus rejection is a decision but not necessarily true, and acceptance is not a decision in any sense of the word.
There is a modern approach in which the terms rejection and acceptance are not used, however this approach is beyond the scope of this post. But it remains true in that the acceptance of a null hypothesis is a weak decision whereas rejection is strong evidence of the sample against the null hypothesis. When the null hypothesis is rejected it means the sample has done some statistical work, but when the null hypothesis is accepted it means the sample is almost silent. The behavior of the sample should not be used in favor of the null hypothesis.