Question

The countries of Europe report that 48% of the labor force is female. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force.

1. The representatives from the department of labor want to estimate the percentage of females in the US labor force with 90% confidence. In a sample of 525 employment records, they found that 229 of the workers were female.  Create the 90% confidence interval.  Show all work. Assume conditions are met. (+4)
2. Interpret the meaning of the confidence interval. (+2)
3. Should the representatives from the Department of Labor conclude that the percentage of females in their labor force is lower than Europe's rate of 48%? (+2)

Answer 1

Let p denote the proportion of females in the US labor force

Thus, point estimate of the population proportion = 229/525 = 0.436

Now, corresponding to 90% confidence interval the critical z score = 1.645

Thus the margin of error =

=

= 0.0356

Thus the 90% confidence interval is (0.436 - 0.0356 , 0.436 + 0.0356)

= (0.401, 0.472)

Yes, the representatives from the Department of Labor should conclude that the percentage of females in their labor force is less than Europe's rate of 48% (Since the confidence interval does not contain the value of 0.48 and the upper limit is less than 0.48)