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QBUS3330 Assignment
Question 1 (25 marks)
Motivated by the looming Paris Olympics, back in 2023 the Australian Institute of Sport (AIS)
had to decide whether to introduce mandatory drug testing for athletes. Knowing that drug
tests are not completely reliable, they want to use decision tree analysis to see whether the
benefits outweigh the costs.
Probabilities:
If an athlete is tested for a particular drug, the test result will either be positive or negative.
However, as these tests are not completely accurate some athletes who are drug free test
positive (a false positive) and some athletes who are drug users test negative (a false
negative). The best data we have available suggests that 8% of all athletes use drugs. 2.5% of
all tests on DF athletes result in false positives and 7.5% of all tests on drug using athletes
result in false negatives.
Monetary Values:
The monetary values are difficult to assess but include the following:
The benefit B from correctly identifying a drug user and banning them.
The direct cost, C1, of a test.
The cost, C2, of violating a non-users privacy by performing the test.
The cost C3, of falsely accusing a non-user and banning them.
The cost C4, of not identifying a drug user and allowing them to participate.
We measure the benefit and costs by indexing them against cost C1, which we assign a value
of minus one (-1). This does not mean the direct cost of testing an athlete is $1, it just means
that we express all other monetary values in multiples of C1. The index values are shown in
Table 1.1 on the following page.
Questions:
1. In Excel create two net benefit pay-off tables that map the net benefit of either testing
(four different states) or not testing (two different states) against the decision to ban
or not ban an athlete. Include the pay-off tables in your report. Note: the first table
should be expressed in index notation (+B, -C1, -C2 etc) while the second table should
state the net benefit in numerical terms based on values indicted in table 3.1. For
example, if a positive test is obtained for a non-drug user and this athlete is banned,
there are three associated costs: Cost of the test (-1), the cost of violating the athlete's
privacy (-2) and cost of falsely accusing the athlete (-50). (6 marks)
2. Calculate the relevant posterior probabilities. Include any Bayes tables generated in
Excel in your report. (4 marks)
