Sampling distributions
Two random samples from the same population give different answers. How far from the truth could either one be?
Where you are 7 inside
What this area is about
A statistic such as a sample mean \bar{x} or a sample proportion \hat{p} changes from one random sample to the next. Its sampling distribution is the pattern of its values over all random samples of one size from one population, drawn the same way: where they center, how far they spread, and what shape they make. That pattern is what tells you how much one sample’s answer is worth.
How these fit together
The idea. Sampling variability and simulating it shows the change from sample to sample, and simulating a sampling distribution turns it into a margin of error.
Judging estimators and draws. Bias and variability of an estimator separates aiming at the parameter from landing close to it. The ten percent condition lets draws without replacement be treated as independent when n \le 0.10\,N.
Results. The sampling distributions of \hat{p} and of \bar{x} give the center and spread, and the conditions under which the shape is close to normal (the large-counts condition for \hat{p}; a normal population or a large sample for \bar{x}). Sampling distribution of a difference does the same for \hat{p}_1 - \hat{p}_2 or \bar{x}_1 - \bar{x}_2 from two independent samples.
A path through it
Sampling variability first. Then simulation, bias and the ten percent condition, in any order. Then the proportion and mean formulas (the mean after the central limit theorem), and the difference last.
Finish here and you can build standard errors and start inference for proportions and for means.