For the use of a test for a certain disease, the sensitivity is 0.89, the specificity...

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For the use of a test for a certain disease, the sensitivity is 0.89, the specificity is 0.94, and the prevalence is 0.008. a. Given that a test is positive, find the probability that a random patient has the disease. b. Draw a tree diagram for a typical sample of 1000 patients. c. Of the cases that are positive, explain why the proportion in error is larger if the prevalence is lower. For the use of a test for a certain disease, the sensitivity is 0.89, the specificity is 0.94, and the prevalence is 0.008. a. Given that a test is positive, find the probability that a random patient has the disease. b. Draw a tree diagram for a typical sample of 1000 patients. c. Of the cases that are positive, explain why the proportion in error is larger if the prevalence is lower.