We began our study of data analysis in Chapter 1 by learning graphical and numerical tools for describing the distribution of a single variable and for comparing several distributions. Our study of the practice of statistical inference begins in the same way, with inference about a single distribution and comparison of two distributions. This chapter focuses on quantitative variables, and Chapter 8 focuses on categorical variables.

Two important aspects of any distribution are its center and spread. If the distribution is Normal, we describe its center by the mean μ and its spread by the standard deviation σ. In this chapter, we consider confidence intervals and significance tests for inference about a population mean μ and the difference between two population means μ1−μ2. They can be used to answer questions such as:

• What is the average time for a delivery robot to bring lunch from Cosi to your university dormitory?
• Using a sample of 51 complex medical parts, does the removal of an optical software option that speeds up the measurement process affect the measurement?
• Based on a study of 46 third-graders, can we conclude a new directed reading program improves reading ability?

Chapter 6 emphasized the reasoning of confidence intervals and significance tests; now we emphasize statistical practice and no longer assume that population standard deviations are known. As a result, we replace the standard Normal sampling distribution with the family of t distributions. The t procedures for inference about means are among the most commonly used statistical methods.