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

To calculate the 90% confidence interval for the proportion of females in the U.S. labor force, we first find the sample proportion (p̂) by dividing the number of females (229) by the total sample size (525), which gives us 229/525 = 0.4362. Then, we use the formula for the confidence interval for a proportion: p̂ ± Z*(√[p̂(1-p̂)/n]), where Z is the Z-score corresponding to the desired confidence level (for 90% confidence, Z ≈ 1.645), p̂ is the sample proportion, and n is the sample size. Plugging in the numbers: 0.4362 ± 1.645*√[0.4362*(1-0.4362)/525] gives us the interval 0.3998 to 0.4722.

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