Math CentralQuandaries & Queries


Question from Mong, a student:

In Tests of Hypothesis, what is the decision when the test statistic we compute from the sample information is exactly equal to the critical value? that is, we reject null hypothesis or do not reject it?


You should decide on your procedure, including the rejection region, BEFORE YOU COLLECT THE DATA. Specifically, if when you set up the test, your decision was to reject the null hypothesis when the test statistic is equal to or less than the critical value, then that is what you do. Otherwise, probability has little meaning. Your question, however, points out one weakness of this way of reporting the outcome of an experiment. It is considerably more informative to report the p-value of the experiment, and to provide an appropriate interpretation. In your case you should probably report that there is evidence for the alternative hypotheses, but more data is required for greater certainty. You might want to check out what Wikipedia has to say about the p-value:


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