EU European Union countries report that 46 of their labor fo

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 the 95% confidence interval for the proportion of females in the U.S. labor force is 0.357 to 0.443. Which of the following is the correct interpretation?

a. The margin of error for the true percentage of females in the U.S. labor force is between 35.7% and 44.3%.

b. We are 95% confident that between 35.5% and 44.3% of the persons in the U.S. labor force is female.

c. The percentage of females in the U.S. labro force is between 35.7% and 44.3%.

d. All sample of size 500 will yield a percentage of females in the U.S. labor force that falls within 35.7% and 44.3%

e. None of these

Please explain your answer in order for me to give you credit

Solution

[ Note: I think 35.5% in option (b) is typo and it is actually 35.7% ]

Option(b) is correct i.e. We are 95% confident that between 35.5% and 44.3% of the persons in the U.S. labor force is female.

The interpretation is that if we observe the proportion of female labors for a large number of times almost in 95% cases we can expect the proportion to be within 0.357 and 0.443 .