Section 7.2 Summary

1. The sampling distribution of the sample proportion $\hat{p}$ for a given sample size $n$ consists of the collection of the sample proportions of all possible samples of size $n$ from the population.
2. According to the Central Limit Theorem for Proportions, the sampling distribution of the sample proportion $\hat{p}$ follows an approximately normal distribution with mean ${\mu }_{\hat{p}}=p$ and standard deviation ${\sigma }_{\hat{p}}=\sqrt{pq/n}$ when both the following conditions are satisfied: $n·p\ge 5$ and $n·q\ge 5$.