Question

A researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.03 for a 95% confidence interval?

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.96/0.03)^2
n = 1067.11

Sample size = 1067 (if rounded to nearest integer)
= 1068 (if rounding is done to next interger)