You think that the population proportion of voters who will vote for your candidate is 0.50

Question

You are the manager of a political campaign. You think that the population proportion of voters who will vote for your candidate is 0.50 (use this for a planning value). Your candidate wants to know what proportion of the population will vote for her. Your candidate wants to know this with a margin-of-error of ± 0.01 (at 95% confidence). How big of a sample of voters should you take?

Answer 1

To find the sample size for a proportion assuming that when know the population proportion we use the following formula

 

n = (z_α/2)²*phat*qhat/E²    round up to the next whole number if needed

 

phat = 0.5, qhat = 1 - phat = 0.5, E = 0.01, α = 1 - CL = 1 - .95 = 0.05, α/2 = 0.025, z_0.025 = 1.96

 

n = (1.96)²*0.5*0.5/(0.01)² = 9604

 

Sample 9604 voters.

 

Your text may use different notations for quantities.

 

z_α/2 is the right tail critical value for you confidence interval, some texts use z*

 

E is margin of error, some texts use ME