What Critical value is
The critical value is a concept used in hypothesis testing in statistics. It is a comparison between the test statistic and the critical value to determine whether or not to reject the null hypothesis.
The following are the steps for determining the critical value:
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State the null and alternative hypotheses.
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Select the level of significance (alpha).
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Calculate the test statistic (e.g. t-statistic, z-statistic, chi-square statistic, etc.)
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Find the critical value for the test statistic based on the level of significance (alpha) and the test statistic.
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Compare the test statistic with the critical value.
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If the test statistic is greater than the critical value, reject the null hypothesis. If it is less than the critical value, accept the null hypothesis.
Examples
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Critical value is used in hypothesis testing to determine the significance of an observed result. For example, in a two-tailed test, the critical value would be the number that marks the boundary between rejecting and failing to reject the null hypothesis.
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Critical value is also used in calculating confidence intervals. For example, if a 95% confidence interval is desired, the critical value would be the z-score associated with a 95% confidence level.