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?
A) 751.67
B) 752
C) 1067.11
D) 1068

Question

Quizplus · Accepted Answer

The formula for minimum sample size needed to estimate a population proportion with a given margin of error is: 
n = (z^2 * p * q) / (E^2) 
Where: 
z = the critical value from the standard normal distribution corresponding to the desired level of confidence (1.96 for 95% confidence) 
p = the estimate of the population proportion (since there is no prior estimate, we use 0.5 for maximum variability) 
q = 1 - p 
E = the desired margin of error 
Plugging in the values, we get: 
n = (1.96^2 * 0.5 * 0.5) / (0.03^2) 
n = 1067.11
Therefore, the minimum sample size needed is 1068. Answer choice D is the closest option to this value.

A Researcher in Campaign Finance Law Wants to Estimate the Proportion