Allow me to introduce myself, my name is Victor Sport and I am the Athletic Director at Sports R' Us High School. We are a large urban high school that is nationally recognized for our sports programs. Recently we discovered
evidence of drug use among some of our athletes. (We have reason to believe that 12% of the high school
athletes have taken a banned substance.) So, we hired an outside agency to design a drug-testing program for
our athletes. The main goal of the program is to reduce the use of banned substances by students who play
sports. We plan to give drug tests to randomly selected student athletes at unannounced times during the
school year.
Our school board is considering various consequences for students who test positive, including required
counseling, suspension from athletic participation and even expulsion. Before deciding on these consequences,
they have asked me to present the program at an upcoming board meeting. I am struggling to understand the
math behind this program, and I need to convince the board (who has zero math skills) that it is doing what is
what designed to do. Your enterprising and resourceful professor has indicated that you will be able to help me
clarify the following:
The testing company tells us the drug test has a false positive rate of 3% and a false negative rate of
10%. I do not understand these terms. What do they mean, and how do they relate to the probability
that a randomly chosen athlete tests positive (or negative) for banned substans?
The worst thing I can imagine is wrongly accusing an athlete and potentially ruining their future. Ifa
randomly chosen athlete tests positive, what is the probability that the student did not take a banned
substance? On the other hand, it's important to catch the offenders. What is the probability that the
student did take a banned substance? Do these probabilities make sense in terms of our goals?
.
One option we are considering is to immediately retest any athlete who tests positive. If a student who
gets a positive result on both tests, they would be suspended for a year. Does this make sense? What is
the likelihood that he actually took a banned substance?
Please help me make sense of this and get ready for the board meeting. Include numerical, graphical, symbolic,
and verbal defense of all your recommendations. That way I can use them to back up my case with the board
(or go back to the testing agency for program changes).
Sincerely,