A Drug test has a sensitivity of 88 and a specificity of 76

A Drug test has a sensitivity of 88% and a specificity of 76%.

These tests are going to be used on 2000 HS students where it is known that 22% use drugs.

To the nearest whole number, how many students at this HS are drug users?

How many HS students use drugs?    Round to the nearest student.

How many non-users are at this HS?   Nearest student.

How many of the students that use drugs should we expect to test positive with this drug test?

How many students that use drugs should we expect to test negative?

How many of the students that don\'t use drug should we expect to test negative?

How many students that don\'t use drugs should we expect to test positive?

What is the PPV of this drug test?

What is the NPV of this drug test?

Solution

To the nearest whole number, how many students at this HS are drug users? How many HS students use drugs? Round to the nearest student.

22% use drugs. Hence, 0.22*2000 = 440 use drugs. [ANSWER]

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How many non-users are at this HS? Nearest student.

Everyone else do not use drugs, so there are 2000 - 440 = 1560 who do not use. [answer]

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How many of the students that use drugs should we expect to test positive with this drug test?

E(positive) = 440*P(true positive) + 1560*P(false positive)

= 440*0.88 + 1560*(1-0.76)

= 761.6 [answer]

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How many students that use drugs should we expect to test negative?

E(negative) = 440*P(false negative) + 1560*P(true negative)

= 440*(1-0.88) + 1560*0.76

= 1238.4 [answer]

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