ABSTRACT
In Chapter 5, we began to move into the realm of inferential statistics. There we considered the following general topics: probability, sampling, and estimation. In this chapter, we move totally into the domain of inferential statistics, where the concepts involved in probability, sampling, and estimation can be implemented. The overarching theme of the chapter is the use of a statistical test to make inferences about a single mean. In order to properly cover this inferential test, a number of basic foundational concepts are described in this chapter. Many of these concepts are utilized throughout the remainder of this text. The topics described include the following: types of hypotheses, types of decision errors, level of signicance (α), overview of steps in the decision-making process, inferences about μ when σ is known, Type II error (β) and power (1 − β), statistical versus practical signicance, and inferences about μ when σ is unknown. Concepts to be discussed include the following: null or statistical hypothesis versus scientic or research hypothesis; Type I error (α), Type II error (β), and power (1 − β); two-tailed versus one-tailed alternative hypotheses; critical regions and critical values; z test statistic; condence interval (CI) around the mean; t test statistic; and t distribution, degrees of freedom, and table of t distributions. Our objectives are that by the end of this chapter, you will be able to (a) understand the basic concepts of hypothesis testing; (b) utilize the normal and t tables; and (c) understand, determine, and interpret the results from the z test, t test, and CI procedures.
