4. There is substantial evidence that long-term survival of African-Americans after kidney transplantation is lower than for Caucasian Americans. Possible reasons for this difference include inferior histocompatibility matching, poor compliance with post-operative treatment regimes, and lower socio-economic status. Medical researchers wanted to determine if racial differences in survival after organ transplantation extended to other racial groups and types of organ transplants. They obtain data from the United Network of Organ Sharing (UNOS) for all liver transplants done between 1988 and 1996. Complete information on donor, recipient, and post-operative outcomes was available for 16,669 individuals. The variable of interest was survival rate of patients after 2 years. The results are presented below. (Based on study by Nair and others. 2002. Effect of race on outcome of orthotopic liver transplantation: a cohort study. the Lancet 359: 287-292). Race African- Asian- Row Alive a 2 yrs V Caucasian American Hispanic American Totals Yes 11287 771 1212 341 13611 Exp p. (0-E) LE Adj. Res. No 2312 271 322 153 3058 Exp P (0-E) /E Adj. Res. Column Totals 13599 1042 1534 494 16669 p. p. P p c. Compute the row and column proportions and enter these values in the spaces provided in the contingency table above. d. Using the Row and Column proportions, compute the "Expected" counts of individuals for each of the cells in the contingency table, assuming Ho is true. Enter these values in the first blank line in each cell. e. For each cell in the contingency table, compute the quantity (O-E) /E. Enter these values in the second blank line in each cell of the table above. f. Sum the values for (O-E)'/E across the cells in the contingency table to compute the X2 test statistic. Enter this value here: X2 = g. What are the degrees of freedom for this analysis? Df = h. Use Appendix Table 8 to determine the approximate p-value associated with the computed X2 statistic. Enter this p-value here: p 14.7 i. Use a computer spreadsheet program to determine the exact p-value associated with the computed X2 statistic (see textbook Ch. 12.1.4). Enter p-value here: p =