a) Find P(false positive); that is, find the probability of randomly selecting one of the subjects who tested positive and getting someone who does not use drugs. b) Find P(false negative); that is, find the probability of randomly selecting someone who tested negative and getting someone who does use drugs. c) Are the probabilities of these wrong results low enough so that job applicants and the Acton Paper Company need not be concerned? Explain your answers.
According to the American Management Association, most U.S. companies now test at least some employees and job applicants for drug use. The U.S. National Institute on Drug Abuse claims that about 15% of people in the 18-25 age bracket use illegal drugs. Allyn Clark, a 21 year-old college graduate, applied for a job at the Acton Paper Company, took a drug test, and was not offered a job. He suspected that he might have failed the drug test, even though he does not use drugs. In checking with the company's personnel department, he found that the drug test has 99% sensitivity, which means that only 1% of drug users incorrectly test negative. Also, the test has 98% specificity, meaning that only 2% of nonusers are incorrectly identified as drug users. Allyn felt relieved by these figures because he believed that they reflected a very reliable test that usually provides good results. But is this really true?
The accompanying table shows data for Allyn and 1,499 other job applicants. Based on those results:
a) Find P(false positive); that is, find the probability of randomly selecting one of the subjects who tested positive and getting someone who does not use drugs.
b) Find P(false negative); that is, find the probability of randomly selecting someone who tested negative and getting someone who does use drugs.
c) Are the probabilities of these wrong results low enough so that job applicants and the Acton Paper Company need not be concerned? Explain your answers.
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