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3. Two different brands of u vaccine are under investigation for approval. For testing the effectiveness. they take two random samples of 200 unvaccinated people each. First group gets vaccine A while the second group gets Vaccine B. 120 people from the rst group taking vaccine A and 90 people from the second group taking vaccine B show immunity from monkeypox. a. Can you conclude that vaccine A is better than vaccine B at 1% signicance? What is the p-value of the test? b. Find the 99% condence interval for the proportion of people who got immunity from vaccine B. c. How many more people need to be tested to estimate for the 95% condence interval the immunity proportion from vaccine B to within 0.05