If you want to be 95 confident of estimating the population

If you want to be 95% confident of estimating the population proportion to within a sampling error of + or - .03, what sample size is needed?

A sample size of _____ is needed. (Round up to the nearest integer.)

Sampling Error = + 0.03

Let the required sample size be n

For no prior estimate we take p = 0.50

Std error = sqrt[p *(1-p)/n] = sqrt[0.5 * (1-0.5)/n] = sqrt[0.25/n]

Margin of error = +0.03

alpha = 1 - 0.95 = 0.05

Critical probability = 1 - alpha/2 = 0.975

Critical value for cumulative probability 0.975 is +1.96

Margin of Error = Critical value * Std Error

0.03 = 1.96 * sqrt(0.25/n)

n = 1067