A study on educational aspirations of high school students (S. Crysdale, Int. J.

Comp. Sociol., 16: 19–36, 1975) measured aspirations using the scale (some high school, high school graduate, some college, college graduate). For students whose family income was low, the counts in these categories 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 aspirations and family income using X2 or G2.

Interpret, and explain the deficiency of this test for these data.

b. Find the standardized residuals. Do they suggest any association pattern?

c. Conduct a more powerful test. Interpret results.