# CHAPTER 25

# Mathematical Statistics

In probability theory we set up mathematical models of processes that are affected by “chance.” In mathematical statistics or, briefly, **statistics**, we check these models against the observable reality. This is called **statistical inference**. It is done by **sampling**, that is, by drawing random samples, briefly called **samples**. These are sets of values from a much larger set of values that could be studied, called the **population**. An example is 10 diameters of screws drawn from a large lot of screws. Sampling is done in order to see whether a model of the population is accurate enough for practical purposes. If this is the case, the model can be used for predictions, decisions, and actions, for instance, in planning productions, buying equipment, investing in business projects, and so on.

Most important methods of statistical inference are **estimation of parameters** (Secs. 25.2), determination of **confidence intervals** (Sec. 25.3), and **hypothesis testing** (Sec. 25.4, 25.7, 25.8), with application to *quality control* (Sec. 25.5) and *acceptance sampling* (Sec. 25.6).

In the last section (25.9) we give an introduction to **regression** and **correlation analysis**, which concern experiments involving two variables.

*Prerequisite:* Chap. 24.

*Sections that may be omitted in a shorter course:* 25.5, 25.6, 25.8.

*References, Answers to Problems, and Statistical Tables:* App. 1 ...

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