A polygraph (lie detector) is an instrument used to determine if the individual
ID: 3130467 • Letter: A
Question
A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 88% reliable. In other words, if an individual lies, there is a 0.88 probability that the test will detect a lie. Let there also be a 0.035 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.
Explanation / Answer
a)
As
Ho: The individual is telling the truth.
Ha: The individual is not telling the truth.
Then a type I error is incorrectly rejecting a true Ho. Here, that is incorrectly saying that the individual is lying, when in fact, she is saying the truth.
Hence,
P(Type I) = P(detected lie|truth said) = 0.035 [ANSWER]
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b)
As
Ho: The individual is telling the truth.
Ha: The individual is not telling the truth.
Then a type II error is incorrectly failing to reject a false Ho. Here, that is incorrectly saying that the individual is telling the truth, when in fact, she is lying.
Hence,
P(Type II) = P(detected truth|lie said) = 1 - 0.88 = 0.12 [ANSWER]