A paper demonstrated the application of Bayess Rule for maki

A paper demonstrated the application of Bayes\'s Rule for making inferences about testosterone abuse among athletes. In a population of 1000 athletes, 200 are illegally using testosterone. Of the users, suppose 100 would test positive for testosterone. Of the non users, suppose 16 would test positive.

a. Given that the athlete is a nonuser, find the probability that a drug test for testosterone will yield a negative result.(This probability represents the specificity of the drug test.)

b.If an athlete tests positive for testosterone, use Bayes\'s Rule to find the probability that the athlete is really doping.(This probability represents the positive predictive value of the drug test.)

Solution

P(Illegally using testosterone) = 200/1000 = 0.2

a.

P(Test is negative/Non user ) = P(non user and test is negative)/P(Non user)

=( (800-16)/1000)/(800/1000)

= 0.98 Answer

b.

P(Athelete is doping /Test is positive ) = P(Doping athelete and test is positive)/P(Test is positive)

=( 100/1000)/(0.2 * (100/200) + 0.8 * (16/800))

= 0.862 Answer

= 0.98 Answer