Peanut allergy is increasingly common in Western countries. A study enrolled infants with a diagnosed peanut sensitivity and randomly assigned them to either avoid or regularly consume peanuts until 60 months of age. At the end of the study, 18 of the 51 children who had avoided peanuts were still allergic to peanuts. In contrast, 5 of the 47 children who had regularly consumed peanuts were still allergic to peanuts. We want to estimate how much difference the two approaches make by using a confidence interval for the difference between the proportions with a peanut allergy at 60 months in the two populations. (a) Which of the choices explains why we cannot use the large sample method?
i. There are exactly 10 successes and failures in each sample. Therefore, we should not use the large-sample confidence interval.
ii. There are more than 10 successes and failures in each sample. Therefore, we should not use the large-sample confidence interval.
iii. There are 10 successes and failures in each sample. Therefore, we should be able to use the large-sample confidence interval.
iv. There are not 10 successes and failures in each sample. Therefore, we should not use the large-sample confidence interval.
(b) Obtain the lower value and upper value for the appropriate 95% plus four confidence interval.

B. Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?

Step-by-step explanation:

Remember we are told there's already a question whether pediatricians should recommend early exposure or avoidance. Thus, the research question should answer these two issues (early exposure or avoidance).

Hence, the question we are asking is: Does early exposure to peanuts in small amounts or complete avoidance of peanuts better reduce peanut allergy in children with a known allergy to peanuts?

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497