Multiple Views of Accuracy Rate Problem


1. Drug tests — in reverse

    Here is a scenario you investigated in a prior project:

    A drug test is 95% accurate for a specific drug. This means that it will be correct for 95% of the people tested with it and incorrect for 5% of the people tested with it.

    We saw that for a population of which 5% uses the drug for which this test is designed, half the people who test positive are in fact non-users. This means that if disciplinary action is taken against anyone testing positive, 50% of those people will be disciplined when they shouldn’t.

    Members of a disciplinary board decide that they cannot use this drug test, and will look for a new test. They want no more than 1% error in the disciplinary actions they take with persons testing positive for this drug. How accurate must the new test be to satisfy their requirement?



A table

Density graph

Contour graph and algebra (requires LiveMath Plugin)

3-d Graph