A pharmaceutical lab is trying to develop a rapid assay for detecting HIV infection. The delay in obtaining results for traditional tests reduces their effectiveness because many patients don't return to learn the results. The challenge is to develop a test that provides results in 10 to 15 minutes and is as accurate as the traditional tests. The results of the assay are eight deepening shades of red, with deeper shades indicating greater likelihood of infection. The test is fast, but is it accurate?

To help answer this question, a laboratory trial was conducted on 2000 blood samples, half of which were infected with HIV and half of which were clean. The results are collected in hivassay.sav. Use ROC Curve to determine at what shade the physician should assume that the patient is HIV-positive.