When we've proven that the hypothesis is false !
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If your observations are not as predicted by the hypothesis, then that is a good reason that the hypothesis should be rejected.
You reject a hypothesis when the outcome of an experiment is either inconsistent with the hypothesis or very unlikely if the hypothesis were true.
alternitive hypothesis
You should reject the null hypothesis.
Be able to reject the null hypothesis and accept the research hypothesis
It means that the experiment is consistent with the hypothesis. It adds to the credibility of the hypothesis.
Probability of failing to reject a false null hypothesis.