(1.6) 8. Medical tests for the presence of drags are not perfect. They often giv
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(1.6) 8. Medical tests for the presence of drags are not perfect. They often give false positice results where the test indicates the presence of the drug in a person who has not used the drug, and false negatives where the test does not indicate the presence of the drug in a person who has actually used the drug. Suppose a certain marijuana drug test gives 13.5 percent false positive positives and 2.5 percent false negatives and that in the general population, 0.5 percent of people actually use marijuana Suppose the principal of a high school with 1000 students believes there is a marijuana drug problem in the school and so decides to give all students this drug test. Further suppose that 50 studeats actually use marijuana and 950 students have never used marijuana. (a) Approximately how many students will get a false-positive result? How many will get a false negative result? (b) Approximately how many students will get "caught" and how many will get away with it" How many will be falsely accused of using mari- juana?Explanation / Answer
Given that
Medical test presents two kind of results
1. False posetive :-presence of drug Who didnt used the drug.
2. false negative:-absence of drug Who actually used the drug.
For a general population when there the actual amount of people who uses drug is =0.5% it indicates the
False positive = 13.5%
False negative = 2.5%
Now we have a similer data of
sample size (n)=1000
No of people actually used drug =50 (0.5% of 1000)
a) number of Student who will get false positive result = 13.5% of 1000=1000*13.5/100 =135
Student who will get false negative result =2.5 % of 1000=1000*2.5/100 =25
b)Total number of student who actually uses drug=50
No of student who will found false negative (absence of drug in the people who actuallly use it )=25
So
No of student who will caught =50-25=25
no of student who will get away =50-25=25
No of Student falsely accused willl be =No of student with false positive result =13.5 of 1000=1000*13.5/100 =135
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