This is on contingency tables and conditional probabilities

1 Problem 1: Contingency Tables - 45 points Consider the following contingency table for a generic factor B with levels 0,1,2 and A with levels 0,1. A B 0 1 2 0 8 10 12 16 22 5 You should use the following critical values for chi-squared tests, and show your work. (show expected counts/whatnot) You may use functions like chisq.test() or fisher.test() or prop.test(). > rbind (df, critical) [, 1] [, 2] [,3] [,4] [,5] [, 6] [,7] [, 8] [,9] [, 10] if 1 . 000000 2. 000000 3. 000000 4. 000000 5.0000 6.00000 7.00000 8.00000 9. 00000 10.00000 critical 3.841459 5.991465 7.814728 9.487729 11.0705 12.59159 14. 06714 15.50731 16.91898 18.30704 1.2 Probabilities What are the estimated conditional probabilities P(A = k|B = 0) for k = 0, 1? What are the estimated marginal probabilities P(A = k) for k = 0, 1? Calculate a 95 % confidence interval for p = P(A = 1) based on the wald test (i.e. asymptotic normal approximation)