Question

Suppose that 300 persons are selected at random from a large population and each person in the sample is classified according to blood type: O, A, B, or AB, and according to Rh: positive or negative. The observed numbers are given below. O A B AB Rh+ 82 89 54 19 Rh- 13 27 7 9 (a) Conduct a Pearson’s chi-square test (at level α = 0.05) to test the hy- pothesis that the two classifications of blood types are independent. (b) Confirm your calculation in (a) using R. > rhp = c(82, 89, 54, 19) > rhn = c(13, 27, 7, 9) > chisq.test(rbind(rhp, rhn), correct=F) (c) Calculate the likelihood ratio statistic for testing independence. To do so, first calculate the maximized likelihood under the full model. Denote it by L1 = supθ∈Ω L(n11,n12,n13,n14,n21,n22,n23,n24;θ). Second, calculate the maximized likelihood under the null hypothesis, i.e., the model that assumes independence. Denote it by L0 = supθ∈Ω0 L0(n11,n12,n13,n14,n21,n22,n23,n24;θ). Third, calculate 2(log(L1) − log(L0)). (d) Compare the test statistic in (c) to Pearson’s chi-square statistic. Un- der the null hypothesis of independence, the likelihood ratio statistic follows a χ2 distribution with 3 degrees of freedom. Based upon the likelihood ratio statistic, would you reject H0 at level α = 0.05?

can anyone help with the c,d part please?

Answer 1