On Mon, Mar 3, 2008 at 10:17 AM, Lisa Honeyman <email@example.com> wrote: > "To determine the reliability of experts used in interpreting the results of polygraph examinations in criminal investigations, 280 cases were studied. The results were: > > True Status > Innocent Guilty > Examiner's "Innocent" 131 15 > Decision "Guilty" 9 125 > > If the hypotheses were H0: suspect is innocent vs. Ha: suspect is guilty, then we could estimate the probability of making a Type II error as: > > (a) 15/280 (b) 9/280 (c) 15/140 (d) 9/140 (e) 15/146
This is very tough indeed! I think there are two answers that are both correct. A Type II error is when you fail to reject a false null. That is, they are actually guilty, but found innocent. So that's 15 cases.
But the question is about the denominator. I think a type II error is a CONDITIONAL probability, so it's only OUT OF the cases where the null really is false. So I would say 15/140 for that reason.
However, I think it's possible to interpret it as being out of ALL 280 people, how many type II errors were made? So 15/280 seems like a reasonable answer too, though I think it would be my second choice.
I hope someone who knows what they're talking about will explain this to me!