10.1 Introduction

Suppose that $X$ is a population of numbers that has an unknown mean $\mu .$ Suppose too that it is not possible to compute $\mu .$ For example, it could be that $X$ is too large to reasonably conduct a census. A hypothesis test on $\mu$ is a process in which a sample from the population $X$ is used to make a decision regarding the value of $\mu .$ The decision will involve choosing between two competing hypotheses, as discussed in the prior chapter, except that the hypotheses will involve statements about the value of $\mu .$ And, as in the prior chapter, in making a decision, there is risk in making an error. But, unlike the prior chapter, it won’t be possible to know whether a mistake has been made, as the true value of $\mu$ remains unknown. Tests on a single population mean are used in making decisions in all data-driven disciplines.