# It is estimated that roughly half of smokers lie when asked about their smoking involvement. Pulse CO-oximeters

## Question:

It is estimated that roughly half of smokers lie when asked about their smoking involvement. Pulse CO-oximeters may be a way to get information about smoking without relying on patients' statements. Pulse CO-oximeters use light that shines through a fingernail, and it measures carbon monoxide in blood. These devices are used by firemen and emergency departments to detect carbon monoxide poisoning, but they can also be used to identify smokers. The accompanying table lists results from people aged 18-44 when the pulse CO-oximeter is set to detect a 6% or higher level of carboxyhemoglobin (based on data from "Carbon Monoxide Test Can Be Used to Identify Smoker," by Patrice Wendling, Internal Medicine News, Vol. 40., No. 1, and Centers for Disease Control and Prevention).

Analyzing the Results
1. False Positive Based on the results in the table, find the probability that a subject is not a smoker, given that the test result is positive.
2. True Positive Based on the results in the table, find the probability that a subject smokes, given that the test result is positive.
3. False Negative Based on the results in the table, find the probability that a subject smokes, given that the test result is negative.
4. True Negative Based on the results in the table, find the probability that a subject does not smoke, given that the test result is negative.
5. Sensitivity Find the sensitivity of the test by finding the probability of a true positive, given that the subject actually smokes.
6. Specificity Find the specificity of the test by finding the probability of a true negative, given that the subject does not smoke.
7. Positive Predictive Value Find the positive predictive value of the test by finding the probability that the subject smokes, given that the test yields a positive result.
8. Negative Predictive Value Find the negative predictive value of the test by finding the probability that the subject does not smoke, given that the test yields a negative result.
9. Confusion of the Inverse Find the following values, then compare them. In this case, what is confusion of the inverse?

• P (smoker | positive test result)
• P (positive test result | smoker)

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