The accompanying table contains the results from experiments with a polygraph in

Question

The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts (a) and (b) below. Are these events unlikely? a. Four of the test subjects are randomly selected with replacement, and they all had true negative test results b. Four of the test subjects are randomly selected without replacement, and they all had true negative test results Click on the icon to view the data table a. The prob is 0.026 (Round to t Polygragh Test Results Is such an A. Yes, Yes O C. No, O D. No, Yes (Lied) 28 (true positive) 13 (false negative) No (Did Not Lie) ositive test result Positive test indicated that the subject lied.) egative test result Polygraph test indicated that the subject did not lie.) (false positive) 32 (true negative)

Explanation / Answer

A) P(true negative) = 32/80 = 2/5

P(all 4 test subjects randomly selected with replacement having true negative test results) = (2/5)4

= 0.0256

B) P(all 4 subjects selected without replacement having true negative test result) = (32/80)x(31/79)x(30/78)x(29/77) = 0.0227

Both events are unlikely as the probability is less than 0.05

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