If you are conducting a survey, you will need to decide on the number of people you need to sample. That, of course, depends upon how confident you want to be and how accurately you want to predict the population proportion based on your survey results. If you want to be 95% confident, that is your level of confidence, C. If you want the population proportion within + or – 2%, that is the margin of error, E, you will accept. With that information, you can find the minimum number of people to be surveyed.
If you have an estimate of the population proportion, use that as p-hat. If you do not have any prior information, use 0.5 as your initial estimate of p-hat as that will give you the largest minimum sample size.
You can do that using StatCrunch (here), but I find it quicker to use my Excel calculator below. Just enter your data in the blue cells and the answer will be in the yellow cell.
Here is the answer to part a, with no prior estimate of p-hat. The sample size is 752.
If you use the estimate of 0.34 instead of 0.5, the minimum sample size decreases to 675. The sample size decreased, which is what you should expect. Using 0.5 as the estimate when you don’t have other information will give the largest sample size.
Download a copy of the workbook here: Minimum Sample Size for Proportion CI V1.00