BST 140.652Problem SetProblem 1. Problem 6 from the previous homework.Problem 2. Problem 12 from the previous homework.Problem 3. Retinitis pigmentosa is a disease which manifests itself via different genetic modes ofinheritance. Cases have been documented with a dominant, recessive, and sex-linkedform of inheritance. It has been conjectured that the form of inheritance is relatedto the ethnic origin of the individual. Cases of the disease have been surveyed in anEnglish and Swiss population with the following results: out of 125 English cases,46 had sex-linked disease, 25 had recessive disease and 54 had dominant disease;out of the 110 Swiss cases, one had sex-linked disease, 99 had recessive disease,and 10 had dominant disease. Based on these data is there a significant associationbetween ethnic origin and genetic type? Analyze and interpret (in words) this data.(10 points)Problem 4. In a study of the association between cigarette smoking and lung cancer, 1,357 malelung cancer patients were compared with 1,357 controls in terms of their cigaretteconsumption as follows:Cigarette Consumption Daily0 1− 5− 15− 25− 50+ TotalLung cancer patients 7 49 516 445 299 41 1,357Controls 61 91 615 408 162 20 1,357Compute the odds ratio and log odds ratio in each of the 5 smoking groups comparedwith non-smokers. Find confidence intervals and graphically display. Comment andinterpret. Can relative risks be estimated. Why or why not.Problem 5. In a retrospective study of the possible effect of blood group on the incidence ofpeptic ulcers, Woolf (1955) obtained data from three cities. The table gives for eachcity data for blood groups 0 and A only. In each city, blood group is recorded forpeptic ulcer subjects and for a control series of individuals not having peptic ulcer.Peptic Ulcer ControlGroup 0 Group A Group 0 Group ALondon 911 579 4578 4219Manchester 361 246 4532 3775Newcastle 396 219 6598 5261a. Compute the odds ratio for each city with a confidence interval. Interpret.b. Suppose that it is required to estimate P(ulcer|A) − P(ulcer|0). What furtherinformation is needed to do this from the current data?1Problem 6. Suppose we wish to compare two treatments for breast cancer, viz., simple mastec-tomy (S) and radical mastectomy (R). We form matched pairs of women who arewithin the same decade of age and with the same clinical condition to receive thetwo treatments and measure their 5-year survival. The results are given (L=lived atleast 5 years, D=died within 5 years) below. Perform an analysis of this data, andinterpret your results.Treatment Treatment Treatment TreatmentPair S Person R Person Pair S Person R Person1 L L 11 D D2 L D 12 L D3 L L 13 L L4 L L 14 L L5 L L 15 L D6 D L 16 L L7 L L 17 L D8 L D 18 L D9 L D 19 L L10 L L 20 L DProblem 7. Suppose we are interested in comparing the effectiveness of 2 different antibiotics Aand B in treating gonorrhea. We match each person receiving antibiotic A with anequivalent person (age within 5 years, same sex) to whom we give antibiotic B andwe ask that these persons return to the clinic within 1 week to see if the gonorrheahas been eliminated.Suppose the results are as follows:For 40 pairs of people both antibiotics are successful.For 20 pairs of people antibiotic A is effective while antibiotic B is not.For 16 pairs of people antibiotic B is effective while antibiotic A is not.For 3 pairs of people neither antibiotic is effective.Perform an analysis to compare the relative effectiveness of the two antibiotics.Interpret your results.Problem 8. Consider a retrospective study with matched pairs. Show that McNemar’s test statis-tic is equivalent to performing a Mantel-Haenszel test for all 2 × 2 tables (with onetable for each