The National Bureau of Economic Research (NBER) is a private, nonprofit, nonpartisan research organization. The NBER provides information for better understanding of how the U.S. economy works. Researchers at the NBER concentrate on four types of empirical research: developing new statistical measurements, estimating quantitative models of economic behavior, assessing the effects of public policies on the U.S. economy, and projecting the effects of alternative policy proposals.

One of the NBER's interests is the median income of people in different regions of the United States. The table at the right shows the annual incomes (in dollars) of a random sample of people (15 years and over) in a recent year in four U.S. regions: Northeast, Midwest, South, and West.

EXERCISES

In Exercises 1-5, refer to the annual incomes of people in the table. Use \(\alpha=0.05\) for all tests.

1. Construct a box-and-whisker plot for each region. Do the median annual incomes appear to differ between regions?

2. Use technology to perform a sign test to test the claim that the median annual income in the Midwest is greater than \(\$ 30,000\).

3. Use technology to perform a Wilcoxon rank sum test to test the claim that the median annual incomes in the Northeast and South are the same.

4. Use technology to perform a Kruskal-Wallis test to test the claim that the distributions of annual incomes for all four regions are the same.

5. Use technology to perform a one-way ANOVA to test the claim that the average annual incomes for all four regions are the same. Assume that the populations of incomes are normally distributed, the samples are independent, and the population variances are equal. How do your results compare with those in Exercise 4?

6. Repeat Exercises 1, 3, 4, and 5 using the data in the table below. The table shows the annual incomes (in dollars) of a random sample of families in a recent year in four U.S. regions: Northeast, Midwest, South, and West.

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Annual income of people (in dollars) Northeast Midwest South West 45,481 25,781 19,946 37,922 31,922 28,326 35,140 31,198 27,750 26,910 33,323 24,129 23,179 34,609 36,008 32,194 24,304 32,945 18,030 34,924 32,216 32,119 24,251 22,491 30,393 30,990 24,581 28,668 28,897 44,317 32,005 42,207 25,981 18,021 37,091 24,465 20,439 42,193 33,866 20,776 40,562 25,054 21,746 28,521 48,863 27,703 26,324 37,422