The null hypothesis is an assumption that nothing has changed or occurred and it represents the status quo. It establishes a starting point in order to test out a new hypothesis. A failed t-test, also known as not rejecting the null, can sometimes be equated with accepting the null but this is not always necessarily true as failure to reject does not necessarily mean acceptance of the assumption.
Rejecting or failing to reject a null depends on whether there was sufficient evidence found in favor or against it during the specified tests conducted by either parties; for example, if a research team conducted an experiment that did not confirm their initial theory or provide any statistical significance between two variables then they would fail to reject it due to lack of sufficient evidence (not because they accepted it). Acceptance requires direct proof that supports the claim while non-acceptance requires only absence of positive evidence in its favour.
Debate if “failing to reject the null” is the same as “accepting the null.”
For instance, an archaeology team might conduct an archaeological dig and fail to find any artifacts indicating presence of human life at that location. In such situation, one cannot make any conclusive statements about humans being present at this location hence they would have failed to reject the initial assumption which was “there are no humans present at this site” but cannot accept it either since there wasno direct proof for its validity as well; therefore negating acceptance as well as rejection . Thus proving why failing to reject isn’t necessarily equal to accepting a null hypothesis.
Whether or not a failed t-test proves the validity of null hypothesis again rests on whether sufficient evidence was found disproving its odds rather than simply lacking enough data points; outcomes like these require more testing before making conclusions and thus do not prove anything conclusively since no significant results were obtained in favour/against both theories.