10.29. Table 10.9 shows the mean number of children in Canadian families, classified by whether the family was English speaking or French speaking and by whether the family lived in Quebec or in another province. Let Y = number of children in family, Xi = primary language of family, and X2 = province (Quebec, others).

(a) Describe the association between Y and X^, based on the overall means in this table.

(b) Describe the association between Y and X], controlling for TQ.

TABLE 10.9 Province English French Quebec 1.64 1.80 Other 1.97 2.14 Overall 1.95 1.85

(c) Explain how it is possible that for each level of province the mean is higher for French speaking families yet overall the mean is higher 10.30. Eighth-grade math scores on the National Assessment of Educational Progress had means of 277 in Nebraska and 271 in New Jersey. For white students the means were 281 in Nebraska and 283 in New Jersey. For black students, the means were 236 in Nebraska and 242 in New Jersey. For other nonwhitc students, the means were 259 in Nebraska and 260 in New Jersey.6

(a) Identify the group variable specifying the two states as the explanatory variable. What is the response variable and the control variable?

(b) Explain how it is possible for New Jersey to have the higher mean for each race yet for Nebraska to have the higher mean when the data are combined. (This illustrates Simpson's paradox.).