14. Bob is 24 years old; he is applying for a job as forklift driver with The Widget Company. The human resources (HR) person informs Bob that he must first be tested for illegal drugs. Bob leaves HR and drives immediately over to the diagnostics lab. Bob fills out the lab's questionnaire and checks "NO" to use of any illegal drug. Bob also checks "NO" when prompted to re report any prescription use of opioids. Background about the test. For USA men of Bob's age, about 8% use marijuana, whereas about 0.3% use any of the other drugs, with heroin (an opiate) at a rate of less than 0.06%, about 20% of that of use of cocaine. The assays used to detect drugs in body fluids have the following sensitivity and specificity (yes, these are actual rates). Results of Bob's test come back positive for opiates, but not for any other illegal drug. Sensitivity Specificity Marijuana 91% 75% Methamphetamine 94% 98% Cocaine 95% 99% Opiates 99.8% 96% a. False negative b. True negative c. False positive d. True positive 15. Bob stated that he doesn't do drugs, and yet the result was positive for opioids. So, is Bob a liar? What is the probability that Bob's results are a TRUE positive? Show your work (e.g., attach pdf of image as needed). Remember: this is a statistics course so your explanation must come from statistics; don't just hand-wave with "logic". Use the numbers from the table and an appropriate probability tree as part of your answer. a. ? 14. Bob is 24 years old; he is applying for a job as forklift driver with The Widget Company. The human resources (HR) person informs Bob that he must first be tested for illegal drugs. Bob leaves HR and drives immediately over to the diagnostics lab. Bob fills out the lab's questionnaire and checks "NO" to use of any illegal drug. Bob also checks "NO" when prompted to re report any prescription use of opioids. Background about the test. For USA men of Bob's age, about 8% use marijuana, whereas about 0.3% use any of the other drugs, with heroin (an opiate) at a rate of less than 0.06%, about 20% of that of use of cocaine. The assays used to detect drugs in body fluids have the following sensitivity and specificity (yes, these are actual rates). Results of Bob's test come back positive for opiates, but not for any other illegal drug. Sensitivity Specificity Marijuana 91% 75% Methamphetamine 94% 98% Cocaine 95% 99% Opiates 99.8% 96% a. False negative b. True negative c. False positive d. True positive 15. Bob stated that he doesn't do drugs, and yet the result was positive for opioids. So, is Bob a liar? What is the probability that Bob's results are a TRUE positive? Show your work (e.g., attach pdf of image as needed). Remember: this is a statistics course so your explanation must come from statistics; don't just hand-wave with "logic". Use the numbers from the table and an appropriate probability tree as part of your answer. a
