Probability Workbook For Dummies

Chapter 11

Sampling Distributions and the Central Limit Theorem

IN THIS CHAPTER

Understanding sampling distributions, their means, and their standard errors

Finding probabilities for the sample mean using (and sometimes not using) the Central Limit Theorem

Examining probabilities involving sample proportions

A sampling distribution is a special distribution made from sample statistics. The sample statistics can be the sample means (averages) or the sample proportions (proportion in the sample with a certain characteristic), for example. They are important because if you are trying to estimate or test a hypothesis about a population parameter (such as the population mean or population proportion), you need to know what the distribution is for all possible results you could get, what the mean is, what the standard deviation is, and how to use it to find probabilities about your own sample mean or proportion.

For example, the sampling distribution of the sample mean is the set of all possible sample means taken from all possible samples of size n from your population. The sampling distribution of the sample proportion is the set of all possible sample proportions taken from all possible ...