A polygraph (lie detector) is an instrument used to determine if
an individual is telling the truth. These tests are considered to
be 99% reliable. In other words, if an individual lies, there is a
0.99 probability that the test will detect a lie. Let there also be
a 0.003 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 a Type I error?
(Round your answer to 3 decimal places.)
b. What is the probability of a Type II error?
(Round your answer to 2 decimal places.)
a)
the probability that the probability that the test detects a lie
when the individual telling the truth
can be considered as the type I error.
That is, the probability of type I error is 0.003
The required probability is = 0.003
b)
the test provides a correct result 99% of times. That is, the test
detects the lie when the individual lies with probability 0.99.
Therefore, the probability of type II error
The required probability is, 1 - 0.990 = 0.010
the probability of Type II error is 0.010
.
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