Populations, Samples, and Inference

The main goal of statistical inference is to learn about a phenomenon of interest by extracting useful information from the available data generated by that phenomenon. A particular case, often occurring in applications, is when we want to learn something about a large population, but the data is available only for its small subset, called a sample. Samples are obtained from populations by performing surveys, interviews, polls, or experiments. They are used for obtaining the desired information about populations. The point of sampling a large population is to reduce the cost and the amount of work it would take to examine the entire population. Although we may not realize it, we perform sampling in our daily lives on a regular basis: when tasting food while cooking, when making a blood test, when watching a movie trailer, etc. Other examples include political polls, health surveys, and audits of financial records, to name but a few. In this chapter, we will discuss how to make inferences from a sample to a population. We will also introduce several fundamental notions and methods of statistical inference that will be used in subsequent chapters.