Pleаse nоte thаt this questiоn cоnsists of five pаrts. You need to show all mathematical calculations/explanations to get the final answer. Just giving the answer without showing work may result in zero for the question. A study enrolled 100 infants with diagnosed peanut allergy. They were randomly split into two halves (i.e. 50 infants in each group). Group 1 was instructed to avoid peanuts, and group 2 was instructed to consume very small amounts of peanuts until 5 years of age. At the end of the study period, 18 kids in group 1 were still allergic to peanuts and 8 kids in group 2 were still allergic to peanuts. Give a point estimate for the difference in population proportions of kids allergic to peanut after avoiding it and after consuming small amounts when they were younger. The research group is interested in testing if the true proportion of kids still allergic at age of 5 after avoiding peanuts is greater than that of those of who regularly consumed small amounts of peanuts. Set up the appropriate null and alternative hypotheses to answer this research question. Calculate the test statistic for the test you set up in part 2. Show the calculations. State the rejection region for this problem using 10% significance level. (Just the critical value is insufficient, state the actual rejection region.) Write the final conclusion in the context of the problem.