A vaccine to prevent severe rotavirus gastroenteritis (diarrhea) was given to African children within the first year of life as part of a drug study. The study reported that of the 3298 children randomly assigned the vaccine, 63 got the virus. Of the 1641 children randomly assigned the placebo, 80 got the virus. (Source: Madhi et al., Effect of human rotavirus vaccine on severe diarrhea in African infants, New England Journal of Medicine, vol.362:289-298, January 28, 2010) a. Find the sample percentage of children who caught the virus in each group. Is the ample percent lower for the vaccine group, as investigators hoped? b. Determine whether the vaccine is effective in reducing the chance of catching the virus. Steps l and 2 of the hypothesis-testing procedure are given. Complete the question by doing the rest of the steps. Step 1: H_0: p_v = p_p (p_v is the proportion of children that got the virus among those who took the vaccine, and p_p is the proportion of children that got the virus among those who took the placebo.) H_0: p_v < p_p Step 2: Although we don't have a random sample, we do have random allocation to groups. p = 63 + 80/3298 + 1641 = 143/4939 = 0.028953 n_p times p = 3298 times 0.028953 = 95.49, which is more than 10 n_p times p = 1641 times 0.028953 = 47.51, which is more than 10 (and the other two products are larger)
