6.9 Rejecting, or Failing to Reject the Null

When the p-value falls below the alpha threshold, we should reject the null hypothesis.  A very low p-value associated with our test statistic suggests that our obtained results are not likely due to random chance. 

When the p-value falls at or above the alpha threshold, we should fail to reject the null hypothesis.  Note here that we can reject the null hypothesis, and we can fail to reject it, but we never “accept” it.  While the distinction might seem trivial at first, it exists for an important reason – we always maintain a spirit of open-mindedness and skepticism.  No matter how good that null hypothesis might look sometimes, we never close the book on alternatives!