A polygraph (lie detector) is an instrument used to determine if the individual
ID: 3041350 • 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 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