Problem #3: A high-risk group of 692 male volunteers was included in a major cli

Question

Problem #3: A high-risk group of 692 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 372 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). S of the vaccinated people and 31 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 z' = r, when there is one degree of freedom). (e) Find the p-value. Separate your answers with a comms The order doesn't mstter Answers correct to 4 decimals. Problem #3(s) Problem #3(b) Problem #3(e): Problem #3(d) Problem #3(e):? test statistiz (correct to 3 decimals) critical value (correct to 3 detimals answer correct to 2 decimals - -valu correct to 4 decimals) Just S ve | | Submit Problem #3 for Gradin

Explanation / Answer

applying chi square test:

a) expected values =20.9653 ;18.0347 ; 351.0347 ; 301.9653

b)test statistic = 18.374

c)critical value =3.841

d)test statistic =4.29

e) p value =0.0000

Observed Oi disease no disease Total vaccine 8 364 372 placebo 31 289 320 Total 39 653 692 Expected Ei=?row*?column/?total disease no disease Total vaccine 20.965 351.035 372 placebo 18.035 301.965 320 Total 39 653 692 chi square =(Oi-Ei)2/Ei disease no disease Total vaccine 8.0180 0.4789 8.497 placebo 9.3209 0.5567 9.878 Total 17.339 1.036 18.374

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