8: Sampling Variability and Sampling Distributions

After asking a question, collecting data, analyzing, and probability, the next step would be inference

Inference

Typically consists of comparing populations (or different in proportions) and means (or difference in means).

Populations

Census will result in the true proportion, represented by \(p\). The estimate proportion, from a sample, is denoted with \(\hat{p}\)

Question

\(p\ne\hat{p}\), as the sampling procedure is not a census, the sample size is different, there could be response bias, and sampling variability

Sampling Distribution

A random sample of size \(n\), repeated every possibile combination of size \(n\), will typically result in a trillions of sample.

Warning

Sample distribution and sampling distributions are different. Sampling distributions are for multiple samples

Estimators

An estimator is a method or formula on some small data to determine the true value. It would be ideal to have it centered around the true value, which would be defined as an unbiased estimator.