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, x1 = primary language of family, and x2 = province (Quebec, others).

(a) Describe the association between y and x1, based on the overall means in this table.

(b) Describe the association between y and x1, controlling for x2.

(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 for English-speaking families. (This illustrates Simpson’s paradox. See Exercise 10.14.)
TABLE 10.9 Province English French Quebec 1.64 1.80 Other 1.97 2.14 Overall 1.95 1.85