Question

Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 individuals. If there is more than a 50% chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.

Answer 1

The correct statement is test is reliable and authentic as the probability of no false positives is more than 0.5

Given that

$H_o:P= 0.50\\\\H_1:P>0.50$

Now following calculations to be done to reach out the conclusion

There is no false positive as

= 100 - 5.5

= 94.5%

$\hat P =0.945, n = 12$

Now

$z = \frac{\hat P - P}{\sqrt\frac{P(1-P)}{n} }\\\\=\frac{0.945-0.5}{\sqrt\frac{0.5\times0.5}{12} } \\\\= 3.08$

So

P value = P(z >3.08) = 0.0010

Therefore we can conclude that test is reliable and authentic as the probability of no false positives is more than 0.5

Learn more about the polygraph test here:

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