Question

The countries of Europe report that 45% 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.

a. The representatives from the department of labor want to estimate the percentage of females in the US labor force with 95% confidence. In a sample of 525 employment records, they found that 219 of the workers were female. Create the 95% confidence interval. Show all work. Assume conditions are met.

Interpret the meaning of the confidence interval.

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 46%?

Answer 1

Given

sample of employment records (n)= 525

number of female workers (x) = 219

population proportion (p) = 45% = 0.45

confidence interval (C.I) = 95% = 0.95

= 0.95 , 1 - = 0.05

Z_/2 = 1.96 = Z

population proportion () = x / n

= 219 / 525 = 0.4171

standard error (SE):

SE = 0.02152

margin of error (ME):

ME = Z*SE

ME = 1.96 * 0.02152

ME = 0.0422

C.I = ME

= 0.4171 0.0422

C.I = (0.3749, 0.4593)

i.e., (37.49% ,45.93%) is the 95% confidence interval for population proportion().

this confidence interval indicates that we can be 95% confident that the true percentage of females in the U.S labor force lies in the interval (37.49% ,45.93%)

Yes ,  The representatives from the Department of Labor conclude that the percentage of females in their labor force is lower than Europe's rate of 46%.

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