Problem #3 : A high-risk group of 754 male volunteers was included in a major cl

Question

Problem #3 : A high-risk group of 754 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). 15 of the vaccinated people and 34 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. (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-?2, when there is one degree of freedom (e) Find the p-value. Separate your answers with a comma. The order doesn't matter. Answers correct to 4 decimals Problem #3(a): Problem #3(b): test statistic (correct to 3 decimals) Problem #3(c): critical value (correct to 3 decimals) Problem #3(d): answer correct to 2 decimals Problem #3(e): p-value (correct to 4 decimals)

Explanation / Answer

3a) expected values =24.1751 ; 347.8249 ;24.8249 ; 357.1751

3b) test statistic =7.351

3c) crtiical value =2.706

3d) z =2.71

e)p value =0.0067

Observed Oi got disease Not got disease Total vaccinated 15 357 372 placebo 34 348 382 Total 49 705 754 Expected Ei=?row*?column/?total got disease Not got disease Total vaccinated 24.1751 347.8249 372 placebo 24.8249 357.1751 382 Total 49 705 754 chi square =(Oi-Ei)2/Ei got disease Not got disease Total vaccinated 3.4822 0.2420 3.724 placebo 3.3910 0.2357 3.627 Total 6.873 0.478 7.351

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