Question 4 [13 marks) Hereditary hemochromatosis [HH] is a recessively inherited genetic disorder resulting from mutations in the HFE gene. There are several possible mutations of different degrees of importance but the disease expresses itself only when at least 2 are present in any one individual. A blood analysis was performed on 3,000 blood samples from newborn babies of Caucasian descent in the state of Michigan, USA. The results showed that 163 of those sampled carried two mutations in the HFE gene. a) What is the proportion in the sample that carry the two mutations of the HFE gene? b) Calculate the 95% condence interval for the proportion of this population that carries two mutations in the HFE gene. Check the data for the necessary conditions and show full working. c] Interpret your interval in context. d] If the researcher wanted to halve [x 1h) the margin of error in the condence interval found, what sample size would be required for the same data and level of condence? No Full re-calculation is required for this answer. e) A nationally accepted level of HFE gene prevalence nationally in non-Caucasians in the Michigan State is 3%. Explain if there is evidence that the Caucasians in Michigan have a different rate or proportion of the mutation to non-Caucasians. NOTE that it is NOT necessary to use a separate test of signicance