Whenever we are testing a statistical hypothesis, if the value of the test statistic falls within the rejection region (critical region) then that causes us to reject the null hypothesis and accept the alternative hypothesis.
Factors on which the rejection/critical region depends:
- The critical region depends first of all on the level of significance chosen by the researcher. For example, if the researcher chooses a level of significance of 5% this means that even if the test statistic falls within the rejection region there is a 5% chance that the null hypothesis is true. That is there is a 5% chance that we make the wrong decision
- The rejection region also depends on whether the test is one tailed or two tailed. If the test is two tailed then the critical region has area divided into two equal parts whereas if the test is one tailed then there is only one single critical region.
Acceptance Region vs Rejection Region:
The rejection region can be plotted on the graph of the probability distribution. The complement of the rejection region is called the acceptance region. If the value of the test statistic falls in the acceptance region then we accept the null hypothesis as true.
Example: Suppose we want to check that a coin is unbiased or not. We want to test this hypothesis by conducting a statistical experiment. Here the null hypothesis will be that the coin is unbiased. We can take toss the coin 100 times and measure the number of times we get heads. We can stipulate that if we get heads more than 70 times then we conclude that the coin is biased. In this case, the number of heads being more than 70 is our rejection region.