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A test statistic is a value calculated from a set of observations.

A critical value depends on a null hypothesis about the distribution of the variable and the degree of certainty required from the test. Given a null hypothesis it may be possible to calculate the distribution of the test statistic. Then, given an alternative hypothesis, it is may be possible to calculate the probability of the test statistic taking the observed (or more extreme) value under the null hypothesis and the alternative. Finally, you need the degree of certainty required from the test and this will determine the value such that if the test statistic is more extreme than the critical value, it is unlikely that the observations are consistent with the hypothesis so it must be rejected in favour of the alternative hypothesis.

It may not always be possible to calculate the distribution function for the variable.

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Q: What is the difference between a test statistic and a critical value?
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How do you find p value with test statistic and critical value?

Normally you would find the critical value when given the p value and the test statistic.


What does the critical value represent?

The critical value is used to test a null hypothesis against an alternative hypothesis at some pre-defined level of significance. A test statistic is calculated from the outcomes of a set of trials and if this test statistic is more extreme than the critical value then the null hypothesis must be rejected in favour of the alternative.


What is the meanings of non critical region in statistics?

Every possible experimental outcome results in a value of the test statistic. The non-critical region is the collection of test statistic values that are associated with acceptance of the null hypothesis.


If the difference between the observed and expected frequencies if the critical value is 9.488 and the computed value is 6.079 do you reject or do not reject the null hypothesis?

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How is the critical region utilized in hypothesis testing?

When you formulate and test a statistical hypothesis, you compute a test statistic (a numerical value using a formula depending on the test). If the test statistic falls in the critical region, it leads us to reject our hypothesis. If it does not fall in the critical region, we do not reject our hypothesis. The critical region is a numerical interval.


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What is the difference between ethical value and value?

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What is the conclusion if the test statistic is the same as the critical value?

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