Chapter 9, Problem T9.3SPT

To determine

To find: the best estimate of the probability that an expert commits a Type-II error.

Answer to Problem T9.3SPT

  $P\left(\text{Type II error}\right)=\frac{15}{140}$

Explanation of Solution

Given:

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

  $\begin{array}{l}{H}_0:\text{Suspect is innocent}\\ H_1:\text{Suspect is guilty}\end{array}$

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

Interpretation: The suspect’s true Status is Guilty, whereas the Examiner’s decision is “Innocent”.

The probability is

  $\begin{array}{c}P\left(\text{Type II error}\right)=P\left("innocent"/Guilty\right)=\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{15}{15+125}\\ =\frac{15}{140}\end{array}$

Hence, the correct option is (c)