## 4.1 Sampling Distributions: Introduction to the Concept

I discuss the concept of sampling distributions (an important statistical concept that underlies much of statistical inference), and illustrate the sampling distribution of the sample mean in a simple example.

## 4.2 The Sampling Distribution of the Sample Mean

I discuss the sampling distribution of the sample mean, and work through an example of a probability calculation. (I only briefly mention the central limit theorem here, but discuss it in more detail in another video).

## 4.3 Introduction to the Central Limit Theorem

I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work … Read more

## 4.4 Deriving the Mean and Variance of the Sample Mean

I derive the mean and variance of the sampling distribution of the sample mean.

## 4.5 Proof that the Sample Variance is an Unbiased Estimator of the Population Variance

A proof that the sample variance (with n-1 in the denominator) is an unbiased estimator of the population variance. In this proof I use the fact that the sampling distribution of the sample mean has a mean of mu and a variance of sigma^2/n. If you need that to be shown as well, I show … Read more

## 4.7 Confidence Intervals for One Mean: Assumptions

A look at the consequences of the violation of the normality assumption, when using the one-sample t procedures to draw inferences about the population mean mu.