Failure to reject null hypothesis and accepting null hypothesis are the same. The reason why I believe so is because the only difference that is there is the lack of evidence. Before rejecting or accepting a hypothesis, it is important that the evidence is considered. The evidence should fulfill the expectations of one of the hypothesis brought forward. The hypothesis depends on prediction and direction. The prediction must be fulfilled and the direction must be in accordance to the hypothesis. Without the evidence that the hypothesis is true, it is rejected. The basis of acceptance or rejection is in the evidence.
Acceptance of the null hypothesis is done when the null hypothesis has enough evidence to be accepted. A null hypothesis is whereby there is no statistical difference between two variables. When you accept a null hypothesis, it means that the alternative hypothesis is rejected. An example of a null hypothesis is weight of a body has no effect on the speed of the body. If this is true, then it is accepted, on basis of evidence, that the weight of a body does not affect its speed. In such a case, a null hypothesis will have been accepted. In case the null hypothesis was rejected then the alternative would be considered true. For the null hypothesis given above, if the given hypothesis is not true, then it will be rejected. This is if the claim if false. The prediction would be false if the weight had a negative impact on the speed of the body.
Miller, F. P., Vandome, A. F., & McBrewster, J. (2009). Statistical Hypothesis Testing. Alphascript Publishing.
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