No(Did not lie) Yes(lied)
positive test result 15(false positive) 42(true positive)
negative test result 32(true negative) 9 (false negative)
Refer to table and assume that one of the 98 test subjects is randomly selected. Find the probability of selecting a subject with a negative test result, given that the subject lied. WHat does this result suggest about the polygraph test?
Given that all the answers are mutually exclusive (total=15+42+32+9=98), i.e. no answer can be counted more than once, and the subject lied with a negative result means that he/she is in the false negative category(9).
So the probability is 9/98.
To find the probability of selecting a subject with a negative test result, given that the subject lied, we need to use the concept of conditional probability.
In this case, we want to find the probability of a negative test result (given that the subject lied). Looking at the table, we can see that there are a total of 98 test subjects.
Out of the 98 test subjects, there are 9 false negatives (subjects who were actually lying but got a negative test result). Therefore, the probability of selecting a subject with a negative test result, given that the subject lied, is 9/98.
Now, let's discuss what this result suggests about the polygraph test. The fact that there are false negatives indicates that the polygraph test is not 100% accurate in detecting lies. In this case, 9 out of the 98 subjects who actually lied were not correctly identified as liars by the test. This suggests that the polygraph test has a false negative rate, meaning it mistakenly identifies some liars as non-liars.
It's important to note that this analysis assumes the given data is accurate and that the table represents the actual results of the polygraph test. However, the interpretation of the result and the conclusions about the polygraph test depend on various factors, such as the sample size and the reliability of the test itself.