(25%) 2. The results of a recent study regarding smoking and three types of illness are shown in the following table. 5 0 Emphysema ] 50 Heart problem 50 Totals 200 (1) If we are interested in determining whether or not illness is independent of smoking. a. State the null and alternative hypotheses to be tested. b. Show the contingency table of the expected frequencies and determine the test statistic. c. Use critical value approach to test for determining if illness is independent of smoking (0L=0.05). What do you conclude? (Give test statistic, rejection rule, and conclusion) (2) If we are interested in determining if the proportions of smokers in the three categories are equal. a. State the null and the alternative hypotheses to be tested. b. Use p-value approach to test for determining if the proportions of smokers in the three categories are equal (a=0_05). What do you conclude? (Give test statistic, rejection rule, and conclusion) A2