A First Course in Statistics, 12th Edition

6.1 The Elements of a Test of Hypothesis

Suppose building specifications in a certain city require that the average breaking strength of residential sewer pipe be more than 2,400 pounds per foot of length (i.e., per linear foot). Each manufacturer who wants to sell pipe in that city must demonstrate that its product meets the specification. Note that we are interested in making an inference about the mean $\mu$ of a population. However, in this example we are less interested in estimating the value of $\mu$ than we are in testing a hypothesis about its value—that is, we want to decide whether the mean breaking strength of the pipe exceeds 2,400 pounds per linear foot.

A statistical hypothesisis a statement about the numerical value of a population ...