## ABSTRACT

When studying inference, we learned that one of the fundamental goals of statistics is to describe some characteristic of a population using the information contained in a sample of observations. In previous chapters in which we were attempting to estimate a mean, the underlying population—such as the serum cholesterol levels of all adult males in the United States—was assumed to be infinite with mean μ and standard deviation σ. From this population, a random sample of size n was selected. The central limit theorem told us that the distribution of the mean of the sample values was approximately normal with mean μ and standard deviation https://www.w3.org/1998/Math/MathML"> σ / n $ \sigma /\sqrt n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429489624/3356e2ed-5dc1-4457-a0c6-203608f5aa7a/content/inline-math22_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . It was critical that the sample was representative of the population so that the conclusions drawn were valid. This chapter provides further detail on some of the important issues regarding sampling theory.