A polygraph (lie detector) is an instrument used to determine if the individual

Question

A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 97% reliable. In other words, if an individual lies, there is a 0.970 probability that the test will detect a lie. Let there also be a 0.009 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 polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 97% reliable. In other words, if an individual lies, there is a 0.970 probability that the test will detect a lie. Let there also be a 0.009 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

Ans:

Type I error

When the null hypothesis is true and you reject it, you make a type I error.

Type II error:

When the null hypothesis is false and you fail to reject it, you make a type II error.

Here,

null hypothesis,H0 :Individual is telling the truth.

P(detect as lie/telling lie)=0.97

P(detect as lie/telling the truth)=0.009

a)P(type I error)=P(reject H0/when H0 is true)=0.009

b)P(type II error=P(fail to reject H0/when H0 is false)

=P(do not detect as lie/telling lie)=1-0.97=0.03

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