A high-risk group of 808 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 328 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). 15 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 5% 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 = x², when there is one degree of freedom). (e) Find the p-value.
A high-risk group of 808 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 328 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). 15 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 5% 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 = x², when there is one degree of freedom). (e) Find the p-value.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1 is half correct, c,d,e are incorrect. C,D,E are a prioroy please expalin in detail
Transcribed Image Text:Problem #3: A high-risk group of 808 male volunteers was included in a major clinical trial for testing a new vaccine for type B
hepatitis. The vaccine was given to 328 persons randomly selected from the group, and the others were injected
with a neutral substance (placebo). 15 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 5% significance level.
Problem #3(b):
(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
=
degree of freedom).
(e) Find the p-value.
Problem #3(a): 19.4851,308.5148,28.5:
1.848
Problem #3(c): 3.815
Problem #3(d): 2.179
Problem #3(e): 4.3823
Separate your answers with a comma.
The order doesn't matter.
Answers correct to 4 decimals.
test statistic (correct to 3 decimals)
critical value (correct to 3 decimals)
answer correct to 2 decimals
p-value (correct to 4 decimals)
x², when there is one
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