(11 points) It is estimated that approximately 8.1 % of Americans are afflicted

Question

(11 points) 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. 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

Ans:

P(disease)=0.081

P(positive/disease)=0.95

P(positive and disease)=0.95*0.081=0.07695

P(positive/not disease)=0.035

P(positive and not disease)=0.035*(1-0.081)=0.032165

P(disease/positive)=P(positive and disease)/P(positive)=100*769.5/1091.15=70.52%

P(disease/negative)=P(negative and disease)/P(negative)=100*40.5/8908.85=0.45%

P(not disease/positive)=100*321.65/1091.15=29.48%

Positive Negative Total Have Diabetes 769.50 40.50 810 Do not have 321.65 8868.35 9190 Total 1091.15 8908.85 10000

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