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$100,000 has been allocated for testing children in a large city for lead poisoning. You have two tests for lead poisoning. A blood test costs $10 for each administration; its sensitivity and specificity equal 1.0. A urine test costs $2 for each administration; its sensitivity equals 0.8, and specificity equals 0.9. Hence 80% of the children who have lead poisoning get positive test results on the urine test, and 10% of the children who do not get positive test results on this test. You estimate that 3% of inner-city children have lead poisoning. Your goal is to allocate the available resources to identify as many of them as possible
Suppose you administer only the blood test. What is the posterior probability of children who have lead poisoning given the positive test result? Approximately how many cases of lead poisoning will it identify?
Suppose you administer only the urine test. What is the posterior probability of children who have lead poisoning given the positive test result? Approximately how many cases of lead poisoning will it identify?
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