# Probability of type 1/type 2 errors and distribution of p-values

1. Oct 18, 2012

### humantripod

Hi,

I had a statistics exam today and there were three questions about which I felt a little uneasy.

The questions which felt too easy involved finding the probability of type 1 and type 2 errors. The scenario was that a lie detector test was given to 1000 people. Of those 1000 people, 500 lied and 500 told the truth. The lie detector incorrectly reported that 185 of the people who were truthtellers were actually lying and that 120 of the liars were telling the truth.

I calculated the P(Type 1 error) by simply doing 185/500 = 0.37
I calculated the P(Type 2 error) by simply doing 120/500 = 0.24

The other question asked me to give the distribution of p-values. I don't recall the question giving any details about whether it was under the assumption that H0 is true or Ha is true, just simply asking for the distribution. I said N(0,1).

What do you think guys? Any mistakes/fundamental flaws in my working out?