The methods of this section assume that sampling is from a population that is very large or infinite, and that we are sampling with replacement. If we have a relatively small population and sample without replacement, we should modify E to include a finite population correction factor, so that the margin of error is as shown in Exercise 37, where N is the population size. That expression for the margin of error can be solved for n to yield

Repeat Exercise 32, assuming that a simple random sample is selected without replacement from a population of 500 people. Does the additional information about the population size have much of an effect on the sample size?

No(za/2) n (N 1)E + o(za/2)