How many students would you have to poll to be 95% confident of the outcome within +/- 2% of the vote?

Question

A school has 1600 students and they are going to vote as to whether they will completely convert the school completely off fossil fuels. How many students would you have to poll to be 95% confident of the outcome within +/- 2% of the vote?

Answer 1

Margin of error = 1.96 sqrt (pq/n)

1.96 (Z score for a 95% confidence interval)

p=q=0.5 as stated by Jon (given no other information)

n is the sample size

So 0.02 = 1.96 sqrt (0.5 x 0.5 / n), giving n=2401 as Jon calculated. (This is correct theory).

Obviously intuitively this isn't sensible, as if we polled all 1600 students we would have perfect information, so a better than 95% confidence interval !

Answer 2

since we don't know the population proportion, we use 0.5.

n = 0.25 ( 1.96/0.02 ) ^ 2 = 2401 (more than the number of students in the school).