Question

To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of $280$such cases was studied. The results were

(a) $15/280$.

(b) $9/280$.

(c) $15/140$.

(d) $9/140$.

(e) $15/146$.

Short answer

The reliability of experts who interpret lie detector tests in criminal investigations is$15/140$.

The correct option is (c) .

Step-by-step solution

Given Information

$H_0$ : Suspect is innocent.

$H_a$ : Suspect is guilty.

Explanation

Type II error: Fail to reject the null hypothesis, when the null hypothesis is false.

Interpretation: The Suspect's true Status is Guilty, while the Examiner's decision is "Innocent".

The probability is the number of favorable outcomes divided by the number of possible outcomes:

$P\left(\text{Type II error}\right)=P(\text{" Innocent"}\mid \text{Guilty})$

$=\frac{\#\text{of favorable outcomes}}{\#\text{of possible outcomes}}$

$=\frac{15}{15+125}$

$=\frac{15}{140}$

Therefore, the correct answer is (C).