# Chapter 1 Sampling

In previous weeks, we have discussed the concept of ** sampling**, which involves randomly selecting a

**of \(n\) units from a given**

*sample***. Why do we do this? Often, we are wanting to learn something about a**

*population***. For example:**

*population**for a given population of people, what is the average cholesterol level?*The problem here is that, especially for very large populations, it would be very difficult, if not impossible, to find out the cholesterol level for every person to then find out what the population average, \(\mu\) was. A much more feasible prospect is to measure the cholesterol level for a

**of people from the**

*sample***. From this**

*population***, we could then calculate the average cholesterol which we would call the**

*sample***and denote \(\bar{x}\). We could then use \(\bar{x}\) to**

*sample mean***the**

*estimate***\(\mu\).**

*population mean*Our hope would be that the ** sample mean** is close to the

**, because it is really the**

*population mean***we are wanting to learn about. However, since the**

*population***is only an**

*sample mean***, we are never really sure how close our**

*estimate***is to the**

*estimate***. However, statistics can help us to know how confident we can be in a given estimate. We can factor in things like variablilty, sample size, and sample design, to help us know how far we can go in drawing**

*true value***about a**

*inferences***from our**

*population***.**

*sample estimates*In order to do this, we need to know what the ** sampling distribution** is. Once we know this, it will be much easier draw conclusions about our

**.**

*estimates*In this Topic, we will discuss these concepts with a focus on the ** sample mean** as it is used to estimate the

**. We will discuss the**

*population mean***, and how we can use this distribution to draw conclusions about our**

*distribution of the sample mean*

*estimates.*