Sampling & Sampling Distributions
We can't test everyone. So we test a sample. But how do we know our sample is good?
Sampling Methods
- Simple Random Sampling: Every member has an equal chance. (e.g., Drawing names from a hat).
- Stratified Sampling: Divide into groups (strata) and sample from each. (e.g., 50 men, 50 women).
- Cluster Sampling: Divide into clusters, pick a few clusters, and test everyone in them.
- Systematic Sampling: Every $k$-th person (e.g., every 10th customer).
Errors
- Sampling Error: The natural difference between sample and population. Can be reduced by increasing sample size.
- Non-Sampling Error: Bias, bad survey design, data entry errors. Cannot be fixed by just adding more people.
Central Limit Theorem (CLT)
The magic of statistics. It states that the distribution of sample means will be approximately Normal if the sample size is large enough ($n \ge 30$), regardless of the population's shape.
$$ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} $$
This is the Standard Error.
Test Yourself
Q1: Which sampling method involves dividing the population into groups and picking a few groups to test fully?