1. Sampling Distribution

2. In a statistical application, we take a random sample from our population. We make measurements on the items in the sample and compute a statistic say .
The value of the statistic depends on which items are selected for the sample. is a random variable. Different samples yield different values of

3. What is a sampling distribution?
The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

4. Statistics Estimate Parameters
For example
The sampling distribution of a statistic lets us understand how good it can be expected to be in estimating a parameter.
We want the sampling distribution to be centered at the value of the parameter and to have little variation.
The standard error of an estimator is the standard deviation of its sampling distribution.
Let’s do an example