Question

Question 4 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. 4.a) Estimate the difference between the two proportions. Write your answer here. You can insert an R chunk to perform calculations if you wish.> 4.b) Use the plus four method to find a 99% confidence interval for the difference between the two groups. 〈Write your answer here. You can insert an R chunk to perform calculations if you wish.> 4c) why would it have been inappropriate to use the large sample method to create a 99% CI? Write your answer here.> 4.d) Perform a two-sided hypothesis test for the difference between the groups. Start by stating the null and alternative hypotheses, then calculate the test statistic, the p-value, and conclude with your interpretation of the p-value. 〈Write your answer here.>

Answer 1

Solution Giuen →-ne end of the study tß at 04 the 51 ie the e comped to 5 at o 47 anomiaed to consmf tremxl 185 可 47 0,352141176-01063829 0.247. : ฑ/ confidence tmteslat s the diffečencel the vrethod mthels umeod , We al tab sccs and 4 sample stąeachup 0-36

5( e 0.187 the di esence 0:364-0137) +[-2576x(T1364]米0636155 to-B7米 0-363157 (0.019 , 0-435) . C:t oud be inappopoiarte to use la sample methed beauefos poepostion 2, np-s, and 1竺:We ase test urde s Ho, test statistic : D2r710355**.64761十 0-106长0499Y147 3 , 065 .

eo sideJ ztes! ià o4 The P.value this Sided z ZP (273.065) -Ο, 0022. see this ts less than, the tarce level o oo me uu4lofevrt evidence to evect Ho and conclude that the popelbtion psepostions ose diffosevt