## 17.1 Introduction

In the decision-making process used in statistics, an assumption is made about the population parameter, and then, based on this assumption, the values expected from the sample statistics can be described.

The expectations about the sample statistic are based around how the statistic (such as a sample mean, or a sample proportion, or a sample odds ratio) is distributed: what values it can take, and how often.

A model is used to describe this sampling distribution. For example, if I deal 15 cards, the statistic could be ‘the proportion of red cards in a hand of 15.’ The model would describe how often we would see 0 red cards in 15, 1 red card in 15, 2 red cards in 15, … up to 15 red cards in 15 (Sect. 15.4).

Under certain circumstances, many different statistics have a similarly-shaped distribution: a bell-shaped (or normal) distribution. We now study this distribution, as it often is the basis for describing what values the statistic can be expected to take, based on the assumption about the population that we begin with.