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Math Help - Picking a test confusion

  1. #1
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    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
    but im not sure how to go about this.
    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.

    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.
    Thanks in advanced
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Daniiel View Post
    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
    but im not sure how to go about this.
    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.

    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.
    Thanks in advanced
    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 $$ Cs are the concentrations in the coat sample and $$ Ws are the concentrations from the window sample, and the $$ ss 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
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