Question: In deciding whether to perform mandatory drug testing, we claimed that it is difficult to justify such testing under reasonable conditions. Check this yourself in the following questions.

a. Drug testing ought to be more attractive if the test is more reliable. Keeping the costs the same as in the example, use Precision Tree's two-way sensitivity tool to see whether the optimal decision (test or not test) changes as the probability of a false positive and the probability of a false negative both change. You can let them vary through some reasonable ranges. Explain the results.

b. Repeat part a, but first double the two monetary values that make the test more attractive: the benefit of identifying a user and the cost of not identifying a user. How do your results differ from those in part a?

c. In this part, keep the probabilities of false positives and false negatives the same, but let the benefits and costs vary. Specifically, let the benefit of identifying a user and the cost of not identifying a user be of the form 25a and 20a, where a is some factor that you can vary. Similarly, let the cost of barring a nonuser and the cost of violating privacy be of the form 50b and 2b. The cost of the test is still 1. (The idea is that large values of a and/or small values of b will make the testing more attractive.) Use PrecisionTree's two-way sensitivity tool to see whether the optimal decision (test or not test) changes for a reasonable range of values of a and b. Discuss your results.