A high-risk group of 754 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 375 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). 6 of the vaccinated people and 37 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 10% significance level.
(a) If we use the contingency table method to test this hypothesis, find the 4 values in the expected table.
(b) Find the value of the test statistic (using the contingency table method).
(c) Find the critical value (using the contingency table method).
(d) Using the z-test for proportions, find the value of the test statistic (and verify that z2 = χ2, when there is one degree of freedom).
(e) Find the p-value.