The sample proportion p-hat as a random variable: mean, standard deviation and approximate normality

What this note covers

1. The sample proportion is random
2. Mean and standard deviation of p-hat
3. When the normal approximation works
4. Standardising a sample proportion
5. How sample size changes precision
6. Reading a simulation correctly
7. Exact and approximate probabilities for p-hat
8. Planning precision through the sampling distribution

8 sections · 10 key terms & formulas · 6 common mistakes