BiostatisticsInstructions: Always show how you set up the problem, in order to receive partial credit for a problem. There are 5 questions.Question 1: (20 points)An experiment was conducted to compare the weights of the combs of roosters fed two different vitamin-supplemented diets. Twenty-eight healthy roosters were randomly divided into two groups, with one group receiving diet I and the other receiving diet II. After the study period the comb weight (in milligrams) was recorded for each rooster. The data are:?DietI73 130 115 144 127 126 112 7668 101 126 49 110 123??DietII80 72 73 60 55 74 67 8975 66 93 75 68 76??a)Suppose you wanted to conduct a nonparametric test to compare these data. Using??a = .05, complete the following:?H0:Ha: (two-sided):Value of test statistic:p-value:Conclusion:b) Suppose the experimenters submitted a scientific paper on their results, and received a number of suggestions from referees. One referee suggests that the underlying distributions are normally distributed, and hence that one should compare the two mean weights. Suppose you investigate comparing means assuming normality. Give the formula for the proper statistic to use, and also the p-value.Formula for test statistic:p-value::Question 2: (20 points)For the population of people who suffer occasionally from migraine headaches, suppose that p = 0.60 is the proportion who get some relief from their symptoms by taking ibuprofen.(a) Let X be the number of individuals in a simple random sample of size 50 from this population who get some relief by taking ibuprofen, and let pˆ be the sample proportion. Find the probability that the value of pˆ is in the interval (0.55, 0.65).(b) Repeat part (a) assuming that a sample of size 200 is used instead of a sample of size 50.Question 3: (20 points)To study the effect of pesticides on birds, a scientist randomly and equally allocatesN= 65…