Math
Sampling distribution of a proportion.
Definition
The probability distribution of all possible sample proportions from samples of a fixed size drawn from a population. It is approximately normal when np ≥ 10 and n(1−p) ≥ 10, centered at the population proportion p.
Examples
Real-world.
- 1 Repeatedly polling 200 voters and recording the proportion who support a candidate each time
- 2 Sampling 100 manufactured parts and recording the proportion that are defective across many samples
Key Fact
Standard error = √(p(1−p)/n)