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# ACMMM174

## 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.
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