In: Statistics and Probability
A high-risk group of 656 male volunteers was included in a
major clinical trial for testing a new vaccine for type B
hepatitis. The vaccine was given to 339 persons randomly selected
from the group, and the others were injected with a neutral
substance (placebo). 10 of the vaccinated people and 40 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% 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. |