What Critical region is
The critical region is used in hypothesis testing. It is the set of values of the test statistic that leads to the rejection of the null hypothesis. It is based on the chosen level of significance (α) and the sampling distribution of the test statistic.
Steps for the Critical Region:
- State the null hypothesis (H0) and the alternative hypothesis (Ha).
- Specify the level of significance (α).
- Compute the test statistic and its sampling distribution.
- Determine the critical value (or values) that corresponds to the chosen level of significance.
- Determine the critical region.
- Make a decision about the null hypothesis.
Examples
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Estimating the variance of a population from a sample: it is necessary to ensure that the sample is randomly drawn from the population, otherwise the results may be biased.
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Calculating confidence intervals: it is important that the underlying assumptions of the estimation method are valid, otherwise the confidence interval may not be accurate.
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Assessing the fit of a model: it is important to ensure that the data used to fit the model is not overly influential, otherwise the results may be inaccurate.