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 a percentage of females in the United States labor force.
a. They select a random sample of 525 employment records, and find that 229 of the people are females. State the conditions needed to build a confidence interval.
b. Interpret the confidence interval in this context. Explain what 90% confidence means in this context.
c. 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%? Explain.