A high-risk group of 794 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 347 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 10% significance level. (a) If we use the contingency table method to test this hypothesis, find the 4 values in the expected table. (answers correct to 4 decimals) (b) Find the value of the test statistic (using the contingency table method). (correct to 3 decimals) (c) Find the critical value (using the contingency table method). (correct to 3 decimals) (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). (correct to 2 decimals) (e) Find the p-value. (correct to 4 decimals)
A high-risk group of 794 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 347 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 10% significance level.
(a) If we use the
(b) Find the value of the test statistic (using the contingency table method). (correct to 3 decimals)
(c) Find the critical value (using the contingency table method). (correct to 3 decimals)
(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). (correct to 2 decimals)
(e) Find the p-value. (correct to 4 decimals)
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