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 20 43 negative test results 35 8 the probability is (round to three decimal places as needed.)

Explanation:

Step1: Define positive predictive value formula

Positive predictive value (PPV) = $\frac{\text{True Positives}}{\text{True Positives}+\text{False Positives}}$. Here, true - positives are the number of subjects who 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 values from the table

True Positives = 43 (subjects who lied and had positive test results), False Positives = 20 (subjects who did not lie but had positive test results).

Step3: Calculate PPV

PPV=$\frac{43}{43 + 20}=\frac{43}{63}\approx0.683$

Answer:

0.683