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.
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.
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.
Take the square root of the number obtained from Step 2.
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.
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.
Remember that a 95 percent confidence interval essentially means you can be 95 percent sure the true population proportion lies within your confidence interval. If you took many samples with the same sample size from your population of interest, the sample proportions would fall within your confidence interval 95 percent of the time, but would be outside the confidence interval 5 percent of the time. If you use a 99 percent interval, you can be more sure the true proportion lies within your interval, but the interval will be larger. Conversely, you get less certainty, but a smaller interval, with a 90 percent confidence interval.