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.