Chapter 8, Problem 87CRE

Self-Employment According to the Bureau of Labor Statistics, $10.1\%$ of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed.

a. Test the hypothesis that the proportion of self-employed workers in this area is different from $10.1\%.$ Use a $0.05$ significance level.

b. After conducting the hypothesis test, a further question one might ask, “What proportion of workers in this area are self-employed?” Use the sample data to find a $95\%$ confidence interval for the proportion of workers who are self-employed in the area from which the sample was drawn. How does this confidence interval support the hypothesis test conclusion?