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.Based on a sample of 500 employment records, representatives from the United States Department of Labor find that 240 are female.What is the margin of error for the 95% confidence interval of the proportion of females in the U.S.labor force?
A)0.022
B)0.044
C)0.036
D)0.056
E)0.089

Question

Quizplus · Accepted Answer

The margin of error for a 95% confidence interval of a proportion is calculated using the formula: $ME = Z * \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score for the desired confidence level (1.96 for 95%), $p$ is the sample proportion, and $n$ is the sample size. Here, $p = \frac{240}{500} = 0.48$, and $n = 500$. Plugging these values into the formula gives: $ME = 1.96 * \sqrt{\frac{0.48 * 0.52}{500}} \approx 0.044$.

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