An allergy to peanuts is increasingly comment in western countries. a randomized controlled trial enrolled infants with a diagnosed peanut sensitivity. infants were randomized to either avoid peanuts or consume them regularly until they reached age 5. at the end of the study 18 out of the 51 randomized to avoidance were allergic to peanuts compared to 5 out of the 47 randomized to consuming them regularly. based on this data, conduct the following:

4.a) estimate the difference between the two proportions.

4. b) use the plus four method to find a 99% confidence interval for the difference
between the two groups.

why would it have been inappropriate to use the large sample method to create
a 99% ci?