You use hypothesis tests to challenge whether some claim about a population is true (for example, a claim that 90 percent of Americans own a cellphone). To test a statistical hypothesis, you take a sample, collect data, form a statistic, standardize it to form a test statistic, and decide whether the test statistic refutes the claim. The following table lays out the important details for hypothesis tests.
Note that for the tests involving the difference of two population values
it’s typical that
You can also use these critical z*-values for hypothesis tests in which the test statistic follows a Z-distribution. If the absolute value of the test statistic is greater than the corresponding z*-value, then reject the null hypothesis.