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 shouldnt.
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?
Contour graph and algebra (requires LiveMath Plugin)