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 statistic. The sample is not aware of our plans. We decide about our hypothesis on the basis of the sample statistic. If the sample does not support the null hypothesis, we reject it on probability basis and accept the alternative hypothesis. If the sample does not oppose the hypothesis, the hypothesis is accepted.
But here ‘accept’ does not mean the acceptance of null hypothesis but 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 rejection of : is a strong decision and it leads us to the acceptance of . But acceptance of is not like the acceptance of . The acceptance of null hypothesis does not give us a certain strong decision. It is a situation which may require some further investigations. At this stage, many factors are to be taken into account. The sample size and certain other things not yet discussed help us to do something more about the null hypothesis 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. This modern approach is beyond the level of this book. But it remains true in its place that acceptance of a null hypothesis is a weak decision whereas rejection is a 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. This behavior of the sample should not be used in favor of the null hypothesis.