PrOblem # 3: A highrisk group of 653 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 413 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). 7 of the vaccinated people and 33 of the nonvaccinated ones later got the disease. We wish to test the hypothesis that the probability of getting type B hepatitis is different (higher or lower) for people who were vaccinated compared with people who were not, using the 1% signicance level. (a) If we use the contingency table method to test this hypothesis, nd the 4 values in the expected table. (b) Find the value of the test statistic (using the contingency table method). ((1) Find the critical value (using the contingency table method). (Cl) Using the ztest for proportions, nd the value of the test statistic (and verify that 22 = x2, when there is one degree of freedom). (e) Find the pvalue. Separate your answers with a comma. Problem #3(a): I:| The order doesn't matter. Answers correct to 4 decimals. Problem #3(b): : test statistic (correct to 3 decimals) Problem #3{c): : critical value (correct to 3 decimals) Problem #3(d): : answer correct to 2 decimals Problem #3(e): : pevaiue (correct to 4 decimals) I Just Save I ' Submit Problem #3 for Grading