Question

A company administers a drug test to its job applicants as a condition of employment; if a person fails the drug test the company will not hire them.

Suppose the drug test is 77% sensitive and 75% specific. That is, the test will produce 77% true positive results for drug users and 75% true negative results for non-drug users. Suppose that 9% of potential hires are use drugs. If a randomly selected job applicant tests positive, what is the probability he or she is a user? Make sure that your answer is between 0 and 1.

Answer #1

As we are given here that: drug test is 77% sensitive
and 75% specific, therefore we have here:

P( + | drugs taken) = 0.77

P( - | drugs not taken) = 0.75

Also, we are given here that:

P( drugs taken) = 0.09, therefore P(drugs not taken) = 1 - 0.09 =
0.91

Using law of total probability, we have here:

P(+) = P( + | drugs taken) P( drugs taken) + P( + | drugs not
taken)P(drugs not taken)

P(+) = 0.77*0.09 + (1 - 0.75)*0.91 = 0.2968

Using Bayes theorem, the probability that he or she is a user given that the test was positive is computed as:

P( drugs taken | +) = P( + | drugs taken)P( drugs taken)/ P(+) = 0.77*0.09 / 0.2968 = 0.2335

**Therefore 0.2335 is the required conditional probability
here.**

Suppose a drug test is 93% sensitive and 89% specific. That is,
the test will produce 93% true positive results for drug users and
89% true negative results for non-drug users. Suppose that 4.5% of
people are users of the drug. If a randomly selected individual
tests positive, what is the probability he or she is a user?

As a condition of employment, Fashion Industries applicants
must pass a drug test. Of the last 400 applicants, 30 failed the
test.
Develop a 95% confidence interval for the proportion of
applicants that fail the test.
____________________________________________________________
Would it be reasonable to conclude that 6% of applicants fail
the drug test? Explain why or why not.
____________________________________________________________

As a condition of employment, Fashion Industries applicants must
pass a drug test. Of the last 400 applicants, 30 failed the test.
a) Develop a 90% confidence interval for the proportion of
applicants that fail the test. b) Would it be reasonable to
conclude that 6% of applicants fail the drug test? Explain why or
why not.

Suppose we assume that 5% of people are drug users. If a person
is a drug user, the result of the test is positive 95% of the time,
and if the person is not a drug user, the result is negative 90% of
the time. A person is randomly selected. What is the probability
that he tests positive for drugs?

As a condition of employment, Fashion Industries applicants must
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QUESTION 5
Imagine a test that's 100% sensitive and 80% specific and it's
testing for something that has a 5% chance of occurring. What's the
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are two ways to get a positive result: a true positive and a false
positive). Express your answer as a value between 0 and 1 to two
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Case Study:
Larson Property Management Company.
Larson Property Management Company is one of the largest property
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