Q.3 - The Practice of Statistics for AP

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) $15/146$.

Step-by-Step Solution

Answer

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

The correct option is (c) .

Step 1: Given Information

$H_0$ : Suspect is innocent.

$H_a$ : Suspect is guilty.

Step 2: 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).