## 18.1 Introduction

The last three chapters introduced tools to apply the decision-making process (Sect. 15.4) used in research:

- Make an
**assumption**about the population*parameter*. - Based on this assumption,
describe what values the sample
*statistic*might reasonably be**expected**from all possible samples. **Observe**the sample data, and see if it seems*consistent*with the expectation, or if it*contradicts*the expectation.

One key observation is that,
under certain conditions,
the variation of many *sample statistics*
(such as the sample mean, etc.)
from sample to sample
can be described *approximately by a normal distribution*.
As a result,
the expected behaviour of these statistics can be
*described*,
so we know what to **expect** from the sample *statistic*.

This has been alluded to before.
In Sect. 15.4,
the sample proportion of red cards in a sample of 15
varied from hand to hand,
and was approximately distributed as a normal distribution.
This is no accident:
**Many sample statistics vary from sample to sample
with an approximate normal distribution**
if certain conditions are met.
This is called the *Central Limit Theorem*.

A *sampling distribution* describes
the distribution of the sample statistic:
How the value of the sample statistic varies from sample to sample for many samples.
The *sampling distribution*
here is a normal distribution.

**Definition 18.1 (Sampling distribution)**A

**sampling distribution**is the distribution of some sample statistic, showing how its value varies from sample to sample.