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Rejection Region Formula:
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The Critical Value Rejection Region defines the range of values for which the null hypothesis is rejected in hypothesis testing. It is calculated based on the mean, critical value, and standard error of the statistic.
The calculator uses the rejection region formula:
Where:
Explanation: The formula calculates the range of values that would lead to rejection of the null hypothesis at a given significance level.
Details: Determining the rejection region is essential for hypothesis testing as it provides a clear decision rule for accepting or rejecting the null hypothesis based on sample data.
Tips: Enter the mean value, critical value from the appropriate distribution table, and standard error of the statistic. All values must be valid numerical values.
Q1: What is a critical value?
A: A critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.
Q2: How do I determine the appropriate critical value?
A: The critical value depends on the significance level (α), the test type (one-tailed or two-tailed), and the degrees of freedom for the test.
Q3: What is standard error?
A: Standard error measures the variability of a sample statistic from the population parameter and is used to calculate confidence intervals and test statistics.
Q4: When should I use a one-tailed vs two-tailed test?
A: Use a one-tailed test when the alternative hypothesis is directional, and a two-tailed test when it is non-directional.
Q5: Can this calculator be used for all types of hypothesis tests?
A: This calculator can be used for any test where the rejection region follows the formula Mean ± Critical × SE, including z-tests and t-tests.