This worksheet allows you to see how both the alpha and P-value method of hypothesis testing works. Setting α determines the critical region (shaded in orange); by adjusting the test statistic you can see whether it falls in the critical or noncritical region. The P-value is computed based on the test statistic and is shown as the green shaded area. The decision whether to reject or not reject is given based on the results of the test.
Move the test statistic to the left and then to the right of the critical value. How does this change the decision? When P-value < α, what is the decision? When the green shaded area is larger than the orange shaded area, what does this signify? Are you more likely or less likely to reject the null hypothesis for smaller values of α?