What Rejection region is
In statistics, a rejection region is the set of values of a test statistic that leads to the rejection of the null hypothesis. Rejection regions are used to decide whether or not to accept or reject the null hypothesis based on the evidence provided by data.
The following are the steps used to construct a rejection region:
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State the null hypothesis (H0) and the alternative hypothesis (Ha).
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Calculate the test statistic from the data.
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Find the distribution of the test statistic under the assumption that the null hypothesis is true.
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Determine the critical region for the desired level of significance.
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Compare the calculated test statistic with the critical region.
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Accept or reject the null hypothesis based on the comparison.
Examples
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A rejection region is used to determine whether to accept or reject a hypothesis in a hypothesis test. For example, in a two-tailed hypothesis test, the rejection region would be the set of values that lie beyond the critical values on both the upper and lower tails of the null distribution.
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Rejection regions can also be used to determine the likelihood of obtaining a certain outcome. For example, in a chi-squared goodness-of-fit test, the rejection region would be the set of values of the chi-squared statistic that are greater than the critical value.