Question

Determine the minimum sample size required in order to estimate p, the population proportion, to within 0.04 with 90% confidence, when a previous study has shown that  p is approximately 0.66. Use this value in your formula for determining sample size.

Answer 1

Solution :

Given that,

= 0.66

1 - = 1 - 0.66 = 0.34

margin of error = E = 0.04

t 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= (1.645 * 0.04)² * 0.66 * 0.34

= 379.52000

Sample size = 380 (rounded)