Question

the table below displays results from experiments with polygraph instruments. find the positive predictive value for the test. that is, find the probability that the subject lied, given that the test yields a positive result.
did the subject actually lie?
no (did not lie) yes (lied)
positive test results 16 45
negative test results 31 11
the probability is
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for positive - predictive value

Positive predictive value (PPV) = $\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}}$. In the context of the polygraph test, true positives are the number of subjects who actually lied and had a positive test result, and false positives are the number of subjects who did not lie but had a positive test result.

Step2: Identify the values from the table

True positives = 45 (subjects who lied and had a positive test result), False positives = 16 (subjects who did not lie but had a positive test result).

Step3: Calculate the positive - predictive value

PPV=$\frac{45}{45 + 16}=\frac{45}{61}\approx0.738$

Answer:

0.738