3. A case-control study examined 134 cancer patients and 134 matched cancer-free controls. Each patient was matched to exactly 1 control1 resulting in 134 pairs. For each pair, the smoking history of both the case and the control were recorded. Below is a summary table of the results. For example, 13 pairs had positive smoking history for both the case and the control; also, 25 pairs had a case with a positive smoking history and a control with a negative smoking history. Control + - Total Case + 13 25 38 Case - 4 92 96 Total 17 11'?r 134 (a) For what proportion of the patient pairs does the case smoking history match the control smoking history? [4 points ] (b) For what proportion of the patient pairs does the case smoking history differ from the control smoking history? [4 points ) (c) Calculate the value of the McNemar test statistic. Report the test statistic and its degrees of freedom.(4 points ) (d) Suppose the McNemar test rejects the null hypothesis in this case at the 0.05 signicance level. "Which of the followhig statements would be correct.[4 points) i. Since the McNemar test rejected the null, we conclude that the probability of a positive smoking history is lower in cases than controls. ii. Since the McNemar test rejected the null, we conclude that the probability of a positive smoking history is higher in cases than controls. iii. Since the McNemar test rejected the null, we conclude that the probability that cases and controls do not match is greater than expected