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Math Help - Student T-Distribution or Gaussian Distribution

  1. #1
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    Student T-Distribution or Gaussian Distribution

    Hey guys

    Ok the background is this, I have 1500 observation and after I "compressed" the data using a stat package, I was given 20 observation.

    The question is, should i be using the Gaussian distribution or the t-distribution with 20dfs? And why?

    Thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
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    IT does NOT depend on the sample size
    IF you know \sigma then you use the normal curve
    IF you do NOT know \sigma then you replace sigma with s and use a t
    IN both cases I am assuming that the underlying distribution is normal.
    NOW if the sample size is large, you can use the central limit theorem to make the test/CI approximately normal.
    And it's n-1=19 dfs
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  3. #3
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    Thanks a lot!!!

    But the standard deviation/variance. Can't we just use the formula and estimate it?
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  4. #4
    MHF Contributor matheagle's Avatar
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    Of course, you use s to estimate sigma.
    Then the dirstibution of

    {\bar X-\mu\over s/\sqrt{n}} is a t with n-1 dfs

    and if you know sigma then

    {\bar X-\mu\over \sigma/\sqrt{n}} is a N(0,1)

    where I'm assuming that the data is from a Normal.
    NOW If the sample size is large, either will be close to N(0,1) no matter if you use sigma or s
    since the CLT is taking over and s approaches sigma with probability one.
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