## 4.2 Distribution of Sample Proportion

#### Sampling Distribution of a Small Proportion

- Recall that

\text { Sample proportion, }\ \hat{p}=\frac{\text { number in population with attribute }}{\text { population size }}

and can be treated as a random variable.

- In a small enough population, we are able to list out all the possible samples, the probability of getting each sample, and therefore the sample proportion.

- Therefore, we are able to construct the probability distribution of \hat{p}.

- The distribution of a statistic which is calculated from a sample (such as the sample proportion) is called a sampling distribution.