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Math Help - Stats help Please!!

  1. #1
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    Stats help Please!!

    There's no way I can figure it out! Please see attachment below..thanks.
    Attached Thumbnails Attached Thumbnails Stats help Please!!-ams.jpg  
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  2. #2
    MHF Contributor matheagle's Avatar
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    Thats actually a fun problem.
    I assume that the population varainces are unknow and you need to pool.
    You have to figure out the chi-squares and obtain a t distribution.
    I will be back tonight if you need help.
    IF we assume we know the pop variances then it's a normal distribution.

    You start with the point estimator

    3\bar X-2\bar Y

    But I do need to know if the pop variances are known, I assume not.
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  3. #3
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    It is def a normal distribution. But we never did anything like this in class that I have no idea how to start.
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  4. #4
    MHF Contributor matheagle's Avatar
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    I know that, but I see a few problems.
    In part two do you really want a CI for \mu_1-\mu_2
    or 3\mu_1-2\mu_2?
    THEN, I think your instructor messed up with the relationship between the pop variances.
    It works either way, but the algebra is nicer if we switch the 2 and the 3.

    You start with the pt estimator that I already mentioned.

    3\bar X-2\bar Y is unbiased for 3\mu_1-2\mu_2

    and it's variance is  9\sigma^2_1+4\sigma^2_2

    It's normal hence

    {(3\bar X-2\bar Y)-(3\mu_1-2\mu_2)\over \sqrt{9\sigma^2_1+4\sigma^2_2}}\sim N(0,1)

    Next use the relationship between the sigma's
    BUT I keep asking, are they known?
    If they are this is the test stat and you use a st normal table putting half of alpha in each table.

    MORE likely the sigma's are unknown and you use the relationship and derive a t stat.
    Here you need to pool the sample variances and obtain the chi-square distribution which replaces the \sigma^2s
    Last edited by matheagle; December 15th 2009 at 07:18 AM.
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  5. #5
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    Quote Originally Posted by matheagle View Post
    I know that, but I see a few problems.
    In part two do you really want a CI for \mu_1-\mu_2
    or 3\mu_1-2\mu_2?
    THEN, I think your instructor messed up with the relationship between the pop variances.
    It works either way, but the algebra is nicer if we switch the 2 and the 3.

    You start with the pt estimator that I already mentioned.

    3\bar X-2\bar Y is unbiased for 3\mu_1-2\mu_2

    and it's variance is  9\sigma^2_1+4\sigma^2_2

    It's normal hence

    {(3\bar X-2\bar Y)-(3\mu_1-2\mu_2)\over \sqrt{9\sigma^2_1+4\sigma^2_2}}\sim N(0,1)

    Next use the relationship between the sigma's
    BUT I keep asking, are they known?
    If they are this is the test stat and you use a st normal table putting half of alpha in each table.

    MORE likely the sigma's are unknown and you use the relationship and derive a t stat.
    Here you need to pool the sample variances and obtain the chi-square distribution which replaces the \sigma^2s
    The variables are not known...I asked the professor. Only hint given. Now what do you do though...I'm completely stuck
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  6. #6
    MHF Contributor matheagle's Avatar
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    Replace one variance with the other using the relationship
    Next obtain a Chi-square distribution.
    Then obtain a t density.

    And I asked last week, is there a typo in part 2?
    WHAT exactly do you want the CI for?
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