Question

The U.S. Department of Labor wants to estimate the percentage of females in the labor force to within ± ​4% with​ 90% confidence. As a planning value they use​ 48%, the reported percentage of females in the labor force of EU​ (European Union) countries.

How many employment records should be​ sampled?

Answer 1

Solution:

Given that,

= 0.48

1 - = 1 - 0.48 = 0.52

margin of error = E = 4% = 0.04

At 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 * 0.48 * 0.52

= 422.13

= 422

n = sample size = 422