# How to Calculate the True Population Proportion

#### 29 SEP 2017

#### CLASS

A true population proportion represents the fraction of people in a certain population who have a given characteristic, such as the proportion of non-traditional students at a university. However, it is often impractical to poll the entire population of interest, so statisticians typically poll a sample of people from the population and calculate the population proportion for the sample. You can calculate a confidence interval for the true population proportion using the sample population proportion. The confidence interval contains two numbers, between which the true proportion should fall.

## 1 Divide the number

Divide the number of people in the sample population who have the characteristic being tested by the total number of people in the sample to get the sample proportion.

## 2 Subtract the sample proportion from one

Subtract the sample proportion from one, and multiply the result by the sample proportion. Divide the result by the total number of people in the population.

## 3 Take the square root

Take the square root of the number obtained from Step 2.

## 4 Multiply the result by 1.96

Multiply the result by 1.96, if you want a 95 percent confidence interval of the true population proportion. Multiply the result by 1.645 for a 90 percent confidence interval, or by 2.575 for a 99 percent confidence interval.

## 5 Subtract the result

Subtract the result of Step 4 from the sample population proportion, then add it to the sample proportion. Record these two numbers as the limits of the confidence interval for the true population proportion for example, (0.234, 0.329). This means the true population proportion should lie somewhere between these two numbers.