Critical Value
Definition
A critical value is a specific value that separates the rejection region from the non-rejection region in hypothesis testing. It is compared to the test statistic to determine whether to reject or fail to reject the null hypothesis.
Analogy
Think of a bouncer at a club who has a specific height requirement for entry. If you're taller than the bouncer's height requirement (the critical value), you get into the club (reject the null hypothesis). If you're shorter, you don't get in (fail to reject the null hypothesis).
Related terms
Test Statistic: A test statistic is a numerical value calculated from sample data that is used in hypothesis testing.
Rejection Region: The rejection region is an area on a distribution where, if the test statistic falls within it, we reject the null hypothesis.
Non-Rejection Region: The non-rejection region is an area on a distribution where, if the test statistic falls within it, we fail to reject the null hypothesis.
"Critical Value" appears in:
Study guides (6)
AP Statistics - 6.3 Justifying a Claim Based on a Confidence Interval for a Population Proportion
AP Statistics - 6.8 Confidence Intervals for the Difference of Two Proportions
AP Statistics - 7.2 Constructing a Confidence Interval for a Population Mean
AP Statistics - 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval
AP Statistics - 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures
AP Statistics - 8.3 Carrying Out a Chi Square Goodness of Fit Test
Additional resources (1)
Practice Questions (8)
- The critical value in a goodness of fit test is obtained from:
- If the chi-square statistic is greater than the critical value in a chi-square goodness of fit test, what can be concluded about the null hypothesis?
- In a chi-square goodness of fit test, when the observed chi-square statistic is 15.72 and the critical value is 12.59, what can be concluded about the null hypothesis?
- What happens to the critical value as the sample size increases?
- What information does the critical value provide in a confidence interval?
- How can you calculate the critical value of a two-sample t-test?
- Which of the following is used to determine the critical value in a confidence interval?
- If the confidence level is 90%, what is the critical value in a one-sample z-interval for a proportion?
Resources
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