Combining probability and hypothesis testing (I don’t know why)

Question

Textbook says it’s C, but I think it’s A:

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

|———————————————————|
| Suspect’s True   Examiner’s Decision |
| Status           “Innocent”    | “Guilty” |
| Innocent       | 131            | 9          |
| Guilty           | 15              | 125      |

 

If the hypotheses are H₀: suspect is innocent versus H_a: suspect is guilty, then we could estimate the probability that experts who interpret lie detec tests will make a Type II error as

 

(A) 15/280

(B) 09/289

(C) 15/140

(D) 09/140

(E) 15/146

 

I don’t understand what in statistics overrides the general rule of probability to consider the whole group unless otherwise stated.

Answer 1

You are only considering the null hypothesis, so you are only dealing with those found guilty and not the entire group.