A polygraph (lie detector) is an instrument used to determine if the individual
ID: 3159237 • 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 94% reliable. In other words, if an individual lies, there is a 0.94 probability that the test will detect a lie. Let there also be a 0.006 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. a. What is the probability of Type I error? (Round your answer to 3 decimal places.) b. What is the probability of Type II error? (Round your answer to 2 decimal places.)
Explanation / Answer
a)
Note that
Ho: The person tells the truth.
Ha: The person does not tell the truth.
As a type I error is incorrectly rejecting Ho, then it is a false lie accusation.
Hence, as given,
P(type I) = 0.006 [ANSWER]
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b)
Note that
Ho: The person tells the truth.
Ha: The person does not tell the truth.
As a type II error is incorrectly failing to reject Ho, then it is a false truth call.
Hence,
P(type II) = 1 - P(lie called a lie) = 1 - 0.94 = 0.06 [ANSWER]