6.19 The sample in Table 6.12 consists of 104 black Americans. A similar table relating income and job satisfaction for white subjects in the same General Social Survey had counts (by row) of (3, 10, 30, 27/7, 8, 45, 39/8, 7, 46, 51/4, 2, 28, 47) for females and (1, 4, 9, 9/1, 2, 37, 29/0, 10, 35, 39/7, 14, 69, 109)

for males. Test the hypothesis of conditional independence between income and job satisfaction,

(a) using a model that treats income and job satisfaction as nominal,

(b) using a model that incorporates the category orderings,

(c) with a generalized CMH test for the alternative that the mean job satisfaction varies by level of income, controlling for gender,

(d) with a generalizedCMHtest not designed to detect any particular pattern of association. Interpret, and compare results, indicating the extent to which conclusions suffer when you do not use the ordinality.