28. A study on educational aspirations of high school students (S. Crysdale, International Journal of Comparative Sociology, Vol. 16. 1975, pp. 19-36) measured aspirations us- ing 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 iniddle, the counts were (11. 52. 23, 22), when family income was high, the counts were (9, 41. 12, 27). Software provides the results shown in Table 8.33 TABLE 8.33 Statistic DF Value Prob Chi-Square 6 8.871 0.181 Statistic Value ASE Gamma 0.163 0.080 Kendall's Tau-b 0.108 0.053

a) Report the value of an ordinal measure of association and use it to summarize the as- sociation.

b) Test independence of educational aspirations and family income using the chi-squared test. Interpret, and explain the deficiency of this test for these data.

c) Find a 90% confidence interval for an ordinal measure. Interpret

d) Conduct an alternative test of independence that takes category ordering into account. Interpret results, and compare to results of the chi-squared test.