Question

4. In developing the vaccine of HIV, neither Alvac nor Aidsvax was found to be effective. Scientists are exploring whether using Alvac as a primer and Aidsvax as a booster will be effective for HIV. The Study is conducted in Thailand with 16,395 individuals from the general (not high-risk) popula- tion. • 74 HIV cases reported in the 8198 individuals receiving placebos. • 51 HIV cases reported in the 8197 individuals receiving the treatment. Let pı and p2 denote the probability of HIV in the placebo and treatment populations, respectively. We hope to test Ho : p1 = P2 versus Hq : 21 > P2. Use the central limit theorem to find the p-value of the test and make a decision based on a = 0.05 level.

Answer 1

1 - nithe. Let, m, & n be the sample wires of individual neceiring placebo & the treatment di & fa be the no. of indimiduals haring av among in these two groups respectively, $i & pz be the population proportion of the cases in the fino groups - individuals reeining, to the treatment respectively. We want to test – Hop, = P2 us to Ha- bi>p2 pi ne tirni, ie 1,2 pooled estimate fa fitta By Cig, we can say ne (5- P2) - (pipa) PP292 N(OL) (1-)( *4 + kg) laated based test on A right X crould be appropriate. We reject to at a level of significance if, obale y Tx. Here abs P = .00903 , p 2 = 100622,8 = .00762 obsd r = (-00903 - 00622-0 1004624(1-100762) 49878197 - 2.0688

Co.05 it to at dala, hiv in bo HIV in a 1064 Hence, obsd retro.o5 Hence, we preject to at level 0.05 ile on the basis of giren dată, we can Conclude that the proposta group of individuals and receining plan & the treatment are not equa level of significance. the proportions of & al at st