Question

How large a sample would be necessary to estimate the true proportion defective in a large population within ±3%, with 95% confidence?

(Assume a pilot sample yields   = 0.12)

Answer 1

Solution:

Given that,

= 0.12

1 - = 1 - 0.12 = 0.88

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= (1.960 / 0.03)2 * 0.12 * 0.88

= 450.73

= 451

n = sample size = 451