Use these results from the \"1-Panel-THC\" test for marijuana use, which is prov

Question

Use these results from the "1-Panel-THC" test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results (Hint: Construct a table similar to the example from lecture note) a. Testing for Mariiuana use How many subjects are included in the study? 2. 1. How many of the subjects had a true negative result? 3. What is the probability that a randomly selected subject had a true negative result? If one of the test subjects is randomly selected, find the probability that the subject tested negative or used marijuana If one of the test subjects is randomly selected, find the probability that the subject tested positive or did not use marijuana. If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana? Find P(Use drugsl Positive test result) by using Bayes' theorem. That is, find the probability that a subject actually uses drugs given that he or she has a positive test result b. c. d. e.

Explanation / Answer

Following is the 2 by 2 table:

(a)

(i)

Number of subjects in study : 300

(ii)

Number of true negative result: 154

(iii)

The probability that a randomly selected subject has a true negative result is:

P(true negative result) = 154/ 300 = 0.5133

(b)

From table we have

P(negative) = 157/300

P(did not use marijuana) = 178/300

P(negative and did not use marijuana) = 154/300

Now,

P(negative or did not use marijuana)=P(negative)+P(did not use marijuana)-P(negative and did not use marijuana) = (157/300) + (178/300) - (154/300) = 0.6033

d)

P(did not use marijuana) = 178/300 = 0.5933

Yes becuase this probability is reasonably high.

e)

P(use marijuana and positive test result) = 119/300

P(positve test result) = 143 /300

P(use drugs |Positive test result) = P(use marijuana | Positive test result) = P(use marijuana and positive test result) / P(positve test result) = 119 /143 = 0.8322

Positive Negative Total Use Marijuana 143-24=119 3 122 Not Use Marijuana 24 157-3=154 178 Toal 143 157 300

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