EU (European Union) countries report that 46% of their labor force is female. The United Nations wants to determine if the percentage of females in the U.S. labor force is
The same. Representatives from the United States Department of Labor select a random
Sample of 525 from over 10,000 employment records on file and find that 229 are female.
The 90% confidence interval for the proportion of females in the U.S. labor force is
A) 0.3998 to 0.4722
B) 0.2747 to 0.5973
C) 0.1776 to 0.6944
D) 0.4235 to 0.5679
E) 0.1243 to 0.7100

Question

Quizplus · Accepted Answer

The confidence interval for the proportion of females in the U.S. labor force can be calculated using the formula for a confidence interval for a proportion: $p \pm z*\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the desired confidence level (for 90% confidence, $z \approx 1.645$), and $n$ is the sample size. Here, $p = \frac{229}{525}$, and $n = 525$. Plugging these values into the formula gives the confidence interval 0.3998 to 0.4722.

EU (European Union) Countries Report That 46% of Their Labor