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Topic: [ap-stat] Type II Error Question wording
Replies: 1   Last Post: Mar 3, 2008 1:58 PM

 Joshua Zucker Posts: 1,450 Registered: 1/30/05
Re: [ap-stat] Type II Error Question wording
Posted: Mar 3, 2008 1:58 PM

On Mon, Mar 3, 2008 at 10:17 AM, Lisa Honeyman <lisa.honeyman@gmail.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!

--Joshua Zucker