The countries of Europe report that 46% of the labor force is female. The United

Question

The countries of Europe report that 46% 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 the percentage of females in the United States labor force with 90% confidence. They randomly sampled 525 employment records and found that 229 of the people are females. Create the confidence interval (show your work) of the percentage of ernployed wormen in the United States.

Explanation / Answer

n = 525

p = 229/525 = 0.4362

z-value of 90% CI = 1.6449

SE = sqrt(p*(1-p)/n)

= sqrt(0.4362*(1-0.4362)/525)

= 0.02164

ME = z*SE = 0.03560

Lower Limit = p - ME = 0.40059

Upper Limit = p + ME = 0.47179

90% CI (0.4006 , 0.4718 ) i.e. (40.06%, 47.18%)

As 46% is included in the interval, the proportion for US workers is not different than Europe

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