A study on educational aspirations of high school students (S. Crysdale, Int. J. Compar. Sociol., 16: 19-36 (1975)) measured aspirations using the scale (some high school, high school graduate, some college, college grad- uate). For students whose family income was low, the counts in these cate- gories were (9,44, 13, 10); when family income was middle, the counts were (11,52,23,22); when family income was high, the counts were (9,41, 12, 27).

a. Test independence of educational aspirations and family income using X or G. Interpret, and explain the deficiency of this test for these data.

b. Calculate the adjusted residuals. Do they suggest any association pattern?

c. Conduct an alternative test that may be more powerful. Interpret results.