A First Course in Statistics, 12th Edition

6.2 Formulating Hypotheses and Setting Up the Rejection Region

In Section 6.1 we learned that the null and alternative hypotheses form the basis for inference using a test of hypothesis. The null and alternative hypotheses may take one of several forms. In the sewer pipe example, we tested the null hypothesis that the population mean strength of the pipe is less than or equal to 2,400 pounds per linear foot against the alternative hypothesis that the mean strength exceeds 2,400—that is, we tested

$$\begin{array}{ll}{H}_0:\mu \le 2,400\hfill & (\text{Pipe does not meet specifications}\text{.})\hfill \\ H_{\text{a}}:\mu >2,400\hfill & (\text{Pipe meets specifications}.)\hfill \end{array}$$

This is a one-tailed (or one-sided) statistical test because the alternative hypothesis specifies that the population parameter (the population mean $\mu$ in this ...