Consider a simple poll that is measuring the proportion of c

Consider a simple poll that is measuring the proportion of citizens that hold a particular political belief. What is a conservative, \"worst case scenario\" sample size if you want the margin of error to be 3.7%?

Sample Size = ?

Solution

Using the worst case scenario i.e., by noting that p(1-p) < = 0.25 and is equal to .25

i.e., when p=.50.   Using p = .50 simplifies the formula to obtain the sample size n = (1.96² /4E² )

given E = 0.037

hence n = (1.96² /4(0.037)² ) = 701.5

i.e., approximately n = 702