# Picking a test confusion

• Aug 20th 2010, 11:43 PM
Daniiel
Picking a test confusion
I have this chemistry stat question.
It has like a story to it, but the bottom line is, theres a guy who had broken glass in his coat, they analyzed what the glass was made up of and compared it to that of the composition of the glass at a crime scene. They want to prove the glass at the crime scene is the same as the glass in his coat with 99% confidence.

It gives the following information
I thought chi square, then i saw they gave the SD so then i thought, i'll just prove them individually untill i find one that isnt 99% true, or till i find they're all 99% confident, but i don't think thats right.
http://img841.imageshack.us/img841/4537/afaf.jpg
Is there a way i can combine all this data, or test that im forgetting to us?
They're all from different distributions so its got me confused.
• Aug 26th 2010, 03:06 AM
CaptainBlack
Quote:

Originally Posted by Daniiel
I have this chemistry stat question.
It has like a story to it, but the bottom line is, theres a guy who had broken glass in his coat, they analyzed what the glass was made up of and compared it to that of the composition of the glass at a crime scene. They want to prove the glass at the crime scene is the same as the glass in his coat with 99% confidence.

It gives the following information
I thought chi square, then i saw they gave the SD so then i thought, i'll just prove them individually untill i find one that isnt 99% true, or till i find they're all 99% confident, but i don't think thats right.
http://img841.imageshack.us/img841/4537/afaf.jpg
Is there a way i can combine all this data, or test that im forgetting to us?
They're all from different distributions so its got me confused.

As usuall ther are many ways of doing this, one is:

The null hypothesis is that the composition of the two glasses is the same, and we assume that the concentrations given this assumption are normally distributed with the given SDs.

put:

$z=\dfrac{\left[\frac{C_{As}-W_{As}}{\sqrt{2}s_{As}}+\frac{C_{Co}-W_{Co}}{\sqrt{2}s_{Co}}+\frac{C_{La}-W_{La}}{\sqrt{2}s_{La}}+\frac{C_{Sb}-W_{Sb}}{\sqrt{2}s_{Sb}}+\frac{C_{Th}-W_{Th}}{s_{Th}}\right]}{\sqrt{5}}$

where the $C$s are the concentrations in the coat sample and $W$s are the concentrations from the window sample, and the $s$s the corresponding SD of the test results (note the SD of the difference is now $\sqrt{2}s$ which is where the $\sqrt{2}$ terms come from.

Now $z$ is a standard normal RV and can be tested appropriatly.

CB