Question

To construct a 95% CI for a proportion (p) of 15% with margin of error = 2%, what is the minimum sample size required? For all sample size calculation, alpha = 0.05 (i.e the confidence level =95%), and the power is 80% (i.e. beta = 0.2).

Answer 1

Solution :

Given that,

= 15% = 0.15

1 - = 1 - 0.15 = 0.85

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 = (  Z_/2 / E)² * * (1 - )

= (1.96 / 0.02)² * 0.15 * 0.85

= 1224.51 = 1225

Sample size = n = 1225