Answer both parts: Please show detailed work. I need to understand how to get th

Question

Answer both parts: Please show detailed work. I need to understand how to get the right answer.

Thanks,

1. (20 pts) (From Weinstein and Fineberg (1980)') Physical abuse of children by their parents is a serious health problem. The potential damage caused by allowing a case of child abuse to go undetected is great, but the costs of falsely accusing a parent are also high. As the pediatrician responsible for a school health program, should you institute a screening program of physical examinations to detect abused children? Clearly your response will depend to a large extent on the fraction of children with positive test results who are actually being abused. The experience of school officials indicates that a careful physical examination will detect 95 percent of abused children. Also, among children not abused, 90 percent are correctly diagnosed as not having been abused. The best information suggests that 3 percent of school children in an average American city are being abused by their parents. a. What is the chance that a child is diagnosed as having been abused? b. Suppose a child is examined and is diagnosed as having been abused. How likely is it that such a child is, in fact, abused? 031b P CA) Decision Analysis, p. 95 and Truxal (1989), Probability Examples, p. 41

Explanation / Answer

Let probability of being abused be A while not abused be P( Not A)

P( Detected Abused) = P( Abused)* P( Detected/ABused) + P( Not Abused)* P( Detected/Not ABused) =0.03*0.95+0.10*0.97=0.1255

b) P( Abused/Detected ABused) = 0.03*0.95/0.1255=0.2271

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