Consider Problem 8. Modify the proportionality results as shown in the following and determine the new results of the decision tree:

a.

b.

Data from problem 8

The worst-case scenario for a baseball player is a lifetime ban. We initially assume there are only two options: test everyone or test no one. We assume monetary assets or costs in our analysis. We define the following:

B = benefit for correctly identifying a steroid user and banning this user from baseball
C₁ = cost of the test, including materials and labor.
C₂ = cost of falsely accusing a nonuser and its consequences.
C₃ = cost of not correctly identifying a steroid user (either by testing or by a false negative).
C₄ = cost of violating privacy.

These costs and benefits are hard to measure, except C₁. We will assume a proportionality relationship between C₁ and each other cost and benefit to help the commissioner in his decision process.

Cost/Benefit Assumptions: