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Question

M Th m.in..tn 2s,na . Tr, Ra n', m. , 0 M YouT put a pic User Settings List Next Grades (1 point) it is estimated that approximately 8.1% of Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes correctly diagnoses 95% of all adults over 40 with diabetes as having the disease and incorrectly diagnoses 3.5% of all adults over 40 without diabetes as having the disease. ems Problem 1 Use this information and a theoretical group of 10,000 Americans to construct a table for this testing scenario. Round all answers and results to two decimal places. Test Positive Test Negative Total Have Diabetes Do not have Diabetes Total 10,000 What percentage of Americans who test positive for diabetes would we expect to actually have the disease? What percentage of Americans who test negative for diabetes would we expect to actually have the disease? What percentage of Americans who test positive will not have the disease?

Explanation / Answer

Percentage of Americans who test positive for diabetes are expected to have diabetes actually, 769.50/(769.50+321.65) = 70.52%

Percentage of Americans who test negative for diabetes actually have diabetes = 40.50/(40.50 + 8,868.35) = 0.45%

Percentage of Americans who test positive will not have the disease = 321.65/(769.50 + 321.65) = 29.48%

Test Positive Test Negative Total Have Diabetes 10000*0.081*0.95=769.5 10000*0.081*(1-0.95)=40.5 810 Do not have Diabetes 10000*(1-0.081)*0.035=321.65 10000*(1-0.081)*(1-0.035)=8868.35 9190 Total 1091.15 8908.85 10000

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