Rejection Region Diagram Maker for Hypothesis Tests

When should you use this tool?

• Use a right-tailed diagram when the alternative hypothesis tests whether a value is greater than the null value.
• Use a left-tailed diagram when the alternative hypothesis tests whether a value is smaller than the null value.
• Use a two-tailed diagram when the alternative hypothesis tests whether a value is different in either direction.
• Use the t distribution when the population standard deviation is unknown and your test uses degrees of freedom.

How the calculator builds the chart

Choose a z test or t test, set alpha, select the tail direction, and optionally enter a test statistic. The tool calculates the critical value, shades the rejection region, and places the observed statistic on the same distribution so the decision rule is visible.

How to read the diagram

If the test statistic falls inside the red shaded region, reject H0 at the selected alpha level. If it stays outside the shaded region, fail to reject H0. For two-tailed tests, alpha is split equally between the left and right tails.

Limits and statistical notes

The t critical values use a standard approximation that is accurate for typical classroom and reporting diagrams. For high-stakes statistical decisions, verify final values with your statistics software or course-approved calculator.