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

First, calculate the proportion of females in the sample:
p_hat = 240/500 = 0.48
Next, determine the standard error of the proportion:
SE = sqrt((p_hat*(1-p_hat))/n) = sqrt((0.48*(1-0.48))/500) = 0.0306
Using a 95% confidence interval, we need to find the z-score that corresponds to a probability of 0.025 in the upper and lower tails of the distribution:
z* = 1.96
Finally, the margin of error is:
ME = z*SE = 1.96*0.0306 = 0.0599
Rounding to the nearest thousandth, the margin of error is 0.060. However, we are only given answer choices rounded to the nearest thousandth, so B, 0.044, is the best choice.

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