Studies of the degree of residential racial segregation often use the segregation index. This is the percentage of nonwhites who would have to change the block on which they live to produce a fully non-segregated city€”one in which the percentage of nonwhites living in each block is the same for all blocks in the city. This index can assume values ranging from 0 to 100, with higher values indicating greater segregation. (The national average for large U.S. metropolitan areas in 2009 was 27, down from 33 in 2000.) The table shows the index for a sample of cities for 2005€“2009, classified by region.

a. Report the mean and standard deviation for each of the four regions.
b. Define notation, and state the hypotheses for one-way ANOVA.
c. Report the F test statistic and its P-value. What do you conclude about the mean segregation indices for the four regions?
d. Suppose we took these data from the Census Bureau report by choosing only the cities in which we know people. Is the ANOVA valid? Explain.

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Segregation index Northeast North CentralSouth West Minneapolis-St. New Paul: 56 San Francisco- Orleans: 64 Oakland: 64 Boston: 67 NY, Long Island, Northern NJ: 79 Detroit: 80 Tapa: 58 Worth: 57 Philadelphia: 69 Chicago: 78M Pittsburgh: 68Milwaukee: 8Atlanta 60 See: 54 Dallas-Ft Miami 6 Los Angeles: 70