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3.   The standard blood test screen for the Human Immunodeficiency Virus (HIV) detects antibodies to the...

3.   The standard blood test screen for the Human Immunodeficiency Virus (HIV) detects antibodies to the virus using a laboratory test known as ELISA (enzyme-linked immunosorbent assay). If the ELISA test is run properly under recommended conditions, it has a sensitivity of 99% and a specificity of 99%.

a) (4 pts) Assume the HIV-ELISA test is administered to a low-risk community of 100,000 people. By low-risk we mean a population which has an HIV prevalence of 1%. Construct the appropriate 2 X 2 table, determine the number of false positives and false negatives, and calculate the positive predictive value of the ELISA test in this population.

b) (4 pts) Assume the same ELISA test with the same sensitivity and specificity is used to screen a high-risk population (a population of 100,000 people with an HIV prevalence of 12%), Construct the appropriate 2 X 2 table, determine the number of false positives and false negatives, and calculate the positive predictive value of the ELISA test.   

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