Test for certain type of drug usage (e.g., steroids) Test result is either “+” o

ID: 3045587 • Letter: T

Question

Test for certain type of drug usage (e.g., steroids)

Test result is either “+” or “-”

Tests are never perfect: false positives and false negatives

5% of all athletes use performance enhancing drugs (e.g., steroids)

3% of all tests on drug-free athletes yield false positives

7% of all tests on drug users yield false negatives

What is the probability of a “+” test?

What is the probability of a “-” test?

What is the probability an athlete is drug free given a “-” test result?

What is the probability an athlete uses drugs given a “+” test result?

What can we conclude from a positive or negative test result?

Is drug testing of athletes effective? Why or Why not?

1) probability of a “+” test =P(+) =P(uses and test positive)+P(does not use and test positive)

=0.05*(1-0.07)+(1-0.05)*0.03=0.075

2) probability of a “-” test =1-P( positive test) =1-0.075 =0.925

3)probability an athlete is drug free given a “-” test result =P( dreg free and negative)/P(negative test)

=0.95*(1-0.03)/0.925=0.9962

4) probability an athlete uses drugs given a “+” test result =P(uses and test positive)/P(test positive)

=0.05*(1-0.07)/0.0725 =0.6414

5) we can colclude froom positive or negative test expectation of a person for being a frug user or not.

as probability of being drug user given test is postiive is not very higher therefore testing is not very effective

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.