1 Studies of the degree of residential segregation between blacks and whites use the segre. gation index, defined as the percentage of nonwhites who would have to change the block on which they live in order to produce a fully nonsegregated city-one in which the per- centage 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 segrega. tion. (The national average was 65 in 1990.) Table 12.25 shows the index for a sample of cities in 1994, classified by region. In no sense is this a random sample, but use it to illus- tale mechanics of one-way ANOVA. The overall mean is 72.75, and F, = 81, = 88, F = 71.4 = 51, with st = 4.69, $2 = 2.58, $34.83,34 = 12.46. Consider the null hypothesis Ho === where ; is the mean for all cities in region i.

TABLE 12.25 Northeast North Central South West Buffalo, NY 84 Gary, IN 91 New Orleans, LA 73 Anchorage, AK 38 Newark, NJ 83 Detroit, MI 89 Orlando, FL 64 Dallas, TX 64 Philadelphia. PA 83 Chicago, IL 87 Miami. FL 75 Anaheim, CA 43 Piusburgh, PA 74 Milwaukee, WI 85 Atlanta, GA 72 Houston, TX 59

a) For the four cities in the Northeast, show that the sum of squares of scores about their mcan is 66.

b) The within sum of squares is 622.0. Show that its degrees of freedom equal 12, and that the within-groups estimate of the variance is 51.8

c) Show that the between sum of squares equals 3107.0, based on 3 degrees of freedom. and the between-groups estimate of variance equals 1035.67.

d) Show that the F test statistic equals 20.0, and show that the P-value is P < .001. What do you conclude about the mean indices"

e) Find the plus and minus part that pertains to each comparison using the Bonferroni method for simultaneous 94% confidence intervals. Compare this to cach difference of means to determine which pairs are significantly different. Construct a diagram to sun- manze