A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 95% reliable. In other words, if an individual lies, there is a 0.95 probability that the test will detect a lie. Let there also be a 0.005 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?

b. What is the probability of Type II error?

c. Discuss the consequences of Type I and Type II errors.

d. What is wrong with the statement, "I can prove that the individual is telling the truth on the basis of the polygraph result."

Question

Mathematics

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28 May, 23:58

A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 95% reliable. In other words, if an individual lies, there is a 0.95 probability that the test will detect a lie. Let there also be a 0.005 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?

b. What is the probability of Type II error?

c. Discuss the consequences of Type I and Type II errors.

d. What is wrong with the statement, "I can prove that the individual is telling the truth on the basis of the polygraph result."

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Answers (1)

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Steve Walsh · Answer 1

a) P (Type I error) = 0.005

b) P (Type II error) = 0.05

c) Both errors may be important, depending on the consequences of the test. A Type I error may appear as guilty a innocent person, as a Type II error will fail to detect a guilty person. Depending on the context, one error could be more dangerous than the other.

In this case the probability of the Type I error seems to be minimized respect to the probability of a Type II error. There is ususally a trade off between them.

d) The statement "I can prove that the individual is telling the truth on the basis of the polygraph result" is not entirely accurate. As there is a not null probability that the test can give wrong answers (Type I and II errors), not everytime the test will be capable of proving that the individual is telling the truth.

Step-by-step explanation:

We have a null hypothesis that states "the individual is telling the truth".

a) A Type I error happens when the null hypothesis is rejected when the null hypothesis is true.

In this context, a Type I error is comitted when the conclusion is that the person is lying when it is telling the truth.

The probability of a Type I error (the test erroneously detects a lie even when the individual is actually telling the truth) is 0.005, as is written in the question.

b) A Type II error happens when the null hypothesis is failed to be rejected, even when the null hypothesis is false.

In this context, the test concludes that the person is telling the truth, even when it is lying.

If an individual lies, there is a 0.95 probability that the test will detect this lie. Then, the probability of a Type II error is 1-0.95=0.05.