The Gini coefficient is a measure of inequality, ranging from 0 to 1, with 0 indicating perfect equality, where everyone earns the same income, and 1 indicating total inequality, where one person earns all of the income. The higher the Gini coefficient, the greater the inequality. Sometimes the coefficient is expressed as a percentage ranging from 0% to 100%. Figure 8.14 shows 90%

confidence intervals for the Gini coefficients for income in the United States between 1967 and 2015.

a. In 2016 the average of the Gini coefficients from random samples of U.S.

residents in all fifty states was .464. If we want to estimate a confidence interval around this point estimate of the Gini coefficient, should we estimate a confidence interval for a proportion or a mean?

b. If the standard deviation for the 2016 Gini coefficient is .32 and the total N for all fifty states is 50,000, estimate the appropriate 90% confidence interval.

Show all of the steps.

c. Figure 8.14 does not include the 2016 confidence interval. Based on your calculation of this confidence interval for Part

b, do the 2015 and 2016 confidence intervals overlap?

d. Based on your answer for Part

c, can we say that income inequality in the United States, as indicated by the Gini coefficient, increased from 2015 to 2016?