If we do not reject the null hypothesis based on sample evidence,we have proven beyond doubt that the null hypothesis is true.

Question

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Failing to reject the null hypothesis based on sample evidence only suggests that we do not have sufficient evidence to reject it at the given level of significance. It does not prove that the null hypothesis is true beyond doubt. There may still be a possibility that the null hypothesis is false but we failed to detect it due to some limitations in the sample or the analysis.

If We Do Not Reject the Null Hypothesis Based on Sample