Question

What sample size is needed to give a margin of error within ±4% in estimating a population proportion with 95% confidence?

Use z-values rounded to three decimal places. 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 = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= (1.960 / 0.04)² * 0.5 * 0.5 = 600.25 = 601

n = sample size = 601