Question

You want to construct a 95% confidence interval to estimate an unknown population proportion with a margin of error of ±2%. What is the minimum necessary sample size that you should obtain?

Answer 1

Solution :

Given that,

= 0.5 ( when estimate is not given than use 0.5)

1 - = 1 - 0.5 = 0.5

margin of error = E =+ / - 2% = 0.02

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 = 1.96

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

= (1.96 /  0.02)² * 0.5 * 0.5

=2401

Sample size = 2401