Question

A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 93% reliable. In other words, if an individual lies, there is a 0.93 probability that the test will detect a lie. Let there also be a 0.040 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.)
  

Answer 1

H0 : the individual is telling the truth

That means,

H0 : the individual is not telling lie

V/s

H1 : the individual is telling lie

A.

Type I error = 0.040

( since, type I error is P(reject H0 when H0 is true),

Here the I error is P(detecting individual is lying when the individual is actually telling truth)

B.

Type II error = 0.07

( since, type II error is P(accept H0 when H1 is true.

Here type II error is P(detecting individual tells truth when actually individual tells lie)

Hence,

Type II error = 1 - power of the test

Type II error = 1 - P(detecting individual tells lies when individual actually tells lie)

Type II error = 1 - 0.93

Type II error = 0.07)