Question

What sample size is needed to give a margin of error within ±1.5% in estimating a population proportion with 95% confidence?

Round your answer up to the nearest integer.

Sample size =

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 1.5% = 0.015

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.015)2 * 0.5 * 0.5

= 4268.44

Sample size =4268 rounded