Critical Region, Critical Values and Significance Level

Hypothesis testing requires the sample statistics—such as proportion, mean, or standard deviation—to be converted into a value or score known as the test statistics.

Assuming that the null hypothesis is true, the test statistic for each sample statistic is calculated using the following equations.

As samples assume a particular distribution, a given test statistic value would fall into a specific area under the curve with some probability.

Such an area, which includes all the values of a test statistic that indicates that the null hypothesis must be rejected, is termed the rejection region or critical region.

The value that separates a critical region from the rest is termed the critical value. The critical values are the z, t, or chi-square values calculated at the desired confidence level.

The probability that the test statistic will fall in the critical region when the null hypothesis is actually true is called the significance level.

In the example of testing the proportion of healthy and scabbed apples, if the sample proportion is 0.9, the hypothesis can be tested as follows.