Point Estimates of Population Proportions

Suppose a population contains an unknown proportion $p$ of individuals who have some characteristic (vote yes, are defective, support a policy, etc.). To estimate $p,$ we draw a random sample of size $n$ and count the number $X$ of sampled individuals with the characteristic.

The sample proportion is

$$\hat{p} = \dfrac{X}{n}.$$

We call $\hat{p}$ a point estimate of $p$ because it produces a single numerical guess for the unknown population proportion.

For example, if a pollster surveys $n=200$ voters and finds $X=86$ supporters of a referendum, then the point estimate of the population proportion of supporters is

$$\hat{p} = \dfrac{86}{200} = 0.43.$$