A GSS that cross-classified income in thousands of dollars (<5,>25) by job satisfaction (very dissatisfied, a little satisfied, moderately satisfied, very satisfied) for black Americans produced a 4 × 4 table having counts, by row, (2, 4, 13, 3 / 2, 6, 22, 4 / 0, 1, 15, 8 / 0, 3, 13, 8).
a. Test independence of job satisfaction and income using X2. Interpret and explain the deficiency of this test for these data. Find the standardized residuals. Do they suggest any association pattern?
b. Conduct a test that treats the variables in a quantitative manner, using scores (3, 10, 20, 35) for income and (1, 3, 4, 5) for job satisfaction. Explain why results differ so much from part (a).