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 19 44 negative test results 33 10 the probability is □. (round to three decimal places as needed.)

Explanation:

Step1: Recall Bayes' theorem formula for positive - predictive value

Positive predictive value (PPV) = $\frac{True\ Positives}{True\ Positives + False\ Positives}$
In the context of the table, 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.
True positives = 44, False positives = 19

Step2: Calculate the positive - predictive value

PPV=$\frac{44}{44 + 19}$=$\frac{44}{63}\approx0.698$

Answer:

0.698