Chapter 9, Problem 3PT

To determine

To verify: The reliability of experts who interpret lie detector tests in criminal investigations.

Answer to Problem 3PT

The answer is $c$ ) $\frac{15}{140}$

Explanation of Solution

Given:

Examiner's Decision	Innocent	Guilty
Innocent"	131	15
"Guilty"	9	125

It is given the hypothesis is $H_0:$ suspect is innocent

  $H_a:$ Suspect is guilty

Now to find the probability of Type II error. That is probability of accepting $H_a:$ when it is false. That is probability of decision is suspect is guilty given he is not guilty.

Let A denote decision is suspect is guilty and B denote he is innocent

  $\begin{array}{cc}P(A/B)& =\frac{P(A\cap B)}{P(B)}\\ & =\frac{15}{140}\end{array}$

So the answer is $c$ ) $\frac{15}{140}$