3. (10 pts) Businesses have a vested interest, and often a legal obligation, to

Question

3. (10 pts) Businesses have a vested interest, and often a legal obligation, to ensure that their work-force is drug free. In response to the demand, tests for marijuana, like Drger's DrugTest 5000, are now available. Like an alcohol breath analyzer, Drger claims that marijuana chemicals can be detected in oral fluids with a sensitivity of 90% and specificity of 75%. Survey results suggest that 10% of working age men report use of marijuana at any time in a one year period. Assume 10,000 men and show your work for the following questions. a. How many true positives are expected for men? b. How many false positives are expected for tested men? c. If a man tests positive, but claims he has never used marijuana, what is the chance that he has lied and is in fact a user of marijuana?

Explanation / Answer

A) P(using Marijuana) = 0.1

Sensitivity = 0.9

Expected number of true positives = p(using marijuana) x sensitivity x number of samples

= 0.1 x 0.9 x 10,000

= 900

B) Number of false positives = (1 - specificity) x p(not using marijuana) x number of samples

= (1 - 0.75) x 0.9 x 10,000

= 2250

C) P(user of marijuana | tested positive) = P(user of marijuana and tested positive) / P(tested positive)

= 900 / (900 + 2250)

= 0.2857

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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