Question

[retro] What does the sampling distribution of the sample means allow us to do?

Answer 1

The sampling distribution of the sample means allows us to use a theorem known as the central limit theorem (CLT).

According to the CLT, if we take enough samples from a population (it does not matter which distribution the population belongs to), the sampling distribution of the sample means will always approximate a normal distribution.

This sampling distribution will have a mean which is equal to the population mean and a standard deviation which is equal to the actual standard deviation divided by the square root of the sample size.

This theorem is extremely powerful and forms a base of modern day inferential statistics, as it allows us to draw inferences about populations by taking enough samples from the population.