The concept of test statistic is found in the theory of hypothesis testing. In a test of hypothesis, the test statistic is a function of the sample data and its value is used to decide whether or not to reject the null hypothesis. If the test statistic falls within a critical region, fixed ex-ante, then the null hypothesis is rejected.
Suppose you observe independent draws from a normal distribution having unknown mean and unknown variance .
Suppose you want to test the null hypothesis that the mean is equal to a specific value :
After selecting a critical regionthe null hypothesis that is rejected if the test statistic falls within this critical region, that is, if
Go to the lecture entitled Hypothesis testing for a rigorous definition of the concept of test statistic.
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