Sampling distributions of means is a way to see how a given sample compares to other samples. The example from Behavioral Sciences Stats was comparing different schools SAT scores.
The big idea here is that when talking about the SAT scores of different schools, you can instead talk about their z-score within the sample distribution.
To determine the z-score of a sample mean, we first calculate the standard error of the mean (e.g. ). Then compute the sample mean’s z-score using: .
Definitions
Sampling Distribution of means : A frequency distribution showing all possible sample means that occur when samples of a particular size are drawn from a population. We know this is a normal distribution due to the Central Limit Theorem. It has the same as the underlying raw score population used to create it.
standard deviation of the sampling distribution : aka stnadard error of the mean