Question

Find the minimum sample size n necessary to estimate a population proportion p with a 95% confidence interval that has a margin of error m = 0.03.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03

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 / 0.03)² * 0.5 * 0.5

= 1067.057

= 1067

n = sample size = 1067