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Statistics and Probability Problem Set 2: Application of Probability in Drug Testing Positive Test Result Negative Test Result [Test shows drug use.) (Test shows no drug use.) EPO 5: 45 5 The subject uses drugs. I can take the risk of trying out combinations of data, materials, methods, and techniques to derive and True Positive) False Negative) test potential solutions to existing problems even at the risk of criticism. The subject does not use 25 480 drugs. (False Positive) (True Negative) APC1: I can resolutely understand, address, and resolve issues or problems in my community. Problems: Assume that 1 of the 555 subjects is randomly selected. Read the text below to understand the context of this task. Then, solve the probability questions related to the given setting. 1. Find the probability of selecting someone who got a false negative result. Who would suffer from a false negative result? Why? Drug Testing for Job Applicants 2. Find the probability of selecting someone who got a false-positive result. Who would suffer from a Approximately 85% of U. S. companies test employees and job applicants for drug use. A common and false positive result? Why? inexpensive (around $50) urine test is the EMIT (enzyme multiplied immunoassay technique) test, which tests for the presence of any of five drugs: marijuana, cocaine, amphetamines, opiates, or phencyclidine. 3. Find the probability of selecting someone who uses drugs. Does the result appear to be reasonable to Most companies require that positive test results be confirmed by a more reliable GC-MS (gas estimate the "prevalence rate"? chromatography-mass spectrometry) test. Find the probability of selecting someone who does not use drugs. Does the result appear to be Like nearly all medical tests, drug tests are sometimes wrong. Wrong results are of two different types: reasonable to estimate the proportion of the adult population that does not use drugs? (1) false-positive results and (2) false-negative results. In our society today, these terms should be clearly understood. A job applicant or employee who gets a false positive result is someone who incorrectly 5. Find the probability of selecting a subject with a positive test result or using drugs. appears to be using drugs when they are not using drugs. This type of mistake can unfairly result in job denial or termination of employment. 6. Find the test sensitivity. Definition of Terms: 7. Find the test specificity. Prevalence: Proportion of the population's condition (such as drug use or disease) being considered. Let's deal with the 50 test results from the subjects who use drugs. False-positive: Wrong test result incorrectly indicates that the subject has a condition when the subject does not. 8. If 2 of these 50 subjects who use drugs are randomly selected with replacement, find the probability False-negative: Wrong test result incorrectly indicates that the subject does not have a condition that the first selected person had a positive test result. The second person chosen had a negative test when the subject does. result. True positive: Correct test result indicates that a subject has a condition when the subject does have 9. Repeat the process in Item 8 by assuming that the two subjects are selected without replacement. the condition. True negative: Correct test result indicates that a subject does not have a condition when the subject does not. Test sensitivity: The probability of a true positive test result, given that the subject has the condition being tested. Test specificity: The probability of a true negative test result, given that the subject does not have the condition being tested. Positive predictive value: Probability that a subject has the condition, given that the test yields a positive result (indicating that the condition is present). Negative predictive value: Probability that the subject does not have the condition, given that the test yields a negative result (indicating that the condition is not present). The table below includes results from 555 adults in the United States