Write down what you know about the sample from the problem. The number of people in the sample is a variable called n. The number of people in the sample who meet the criteria is a variable called x.
Calculate the proportion of the sample that meets the criteria by diving x by n with the scientific calculator. Then write it as a variable called p-hat, written as a p with a caret (^) on top of it.
Calculate the proportion of the sample that does not meet the criteria by expressing p^ as a decimal number and subtracting it from the number 1. Write this result down as a variable called q-hat, with the same caret mark as p-hat.
Calculate the size of the standard deviation of p-hat. Multiply p-hat by q-hat. Then divide that result by n. Then take the square root of that result. This variable is typically expressed as Sigma, sub p-hat, which is written with the Greek letter sigma followed by p-hat in subscript. Because sigma is not a character on computers, Sigma, sub p-hat will be expressed as the variable D.
Look up the range number of standard deviations for the confidence interval you are solving for on the Z-table.
Multiply the Z-value by the standard deviation size (D) and express the result as a percentage. This result is known as the sampling error. It can now be said with certainty that the sample proportion is within that certain percentage plus or minus the true population proportion.
Calculate the range of the confidence interval. To calculate the lower bound of the interval, write the sample proportion as a decimal number and subtract the sampling error as a decimal number. To calculate the upper bound of the interval, write the sample proportion as a decimal number and add the sampling error as a decimal number. These upper and lower bound values are usually written in parenthesis, separated by a comma. This is the final answer.