Problem # 3: A high-risk group of 652 male volunteers was included in a major cl

Question

Problem # 3: A high-risk group of 652 male volunteers was included in a major clinical trial for testing a new vaccine for type B hepatitis. The vaccine was given to 352 persons randomly selected from the group, and the others were injected with a neutral substance (placebo). 18 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 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-test for proportions, find the value of the test statistic (and verify that ? when there is one degree of freedom). e) Find the p-value. Separate your answers with a comma The order doesn't matter Problem #3(a): Problem #3(b); Problem #3(c): Problem #3(d) Problem #3(e): 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)

Explanation / Answer

Problem # 3

Total placebo = 652 - 352 = 300

Here the contigency table is given below

(a) Here expected value for any cell

i.e. for diseased and for vaccinated = 52 * 352/652 = 28.07

i.e for diseased and not vaccinated = 52 * 300/652 = 23.93

so the 4 values are

28.07, 23.93, 323.93, 276.07

(b) Value of Test statistic

X2 = ( 18 - 28.07)2/28.07 + (34 - 23.93)2/23.93 + (334 - 323.93)2 + (266 - 276.07)2 = 8.537

(c) Here critical value for dF = 1 and alpha = 0.01

X20.01,1 = 6.635

(d) Here now employing z test

the proportion for diseases in vaccinated p1^ = 18/352 = 0.0511

proportion for diseasess in placebo p^2 = 34/300 = 0.1133

Here pooled deviation p = (18 + 34)/652 = 0.0798

HEre standard error of proportion = sqrt [p* (1-p) * (1/n1 + 1/n2)] = sqrt [0.0798 * (1- 0.0798) * (1/352 + 1/300)] = 0.0213

Test statistic

Z = (0.1133 - 0.0511)/ 0.0213 = 2.9218

Z2 = 2.92182  = 8.537 = X2

(e) p - value = 0.0035

Vaccinated Yes Placebo Total Diseased Yes 18 34 52 No 334 266 600 Total 352 300 652

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.