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Math Help - sampling distribution

  1. #1
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    sampling distribution

    Hello
    I'm working on a homework question and I am looking for some assistance.
    The question refers back to another, but I believe this is all the information below.

    n = 20
    variance = 1.4
    let S^2 denote the sample variance of the 20 measurements

    a) find b such that P(S^2 < b) = .975
    b) find a such that P(a < S^2) = .975

    the answers are given in the back, which are
    a) 2.42
    b) 0.656
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  2. #2
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    Quote Originally Posted by chrisc View Post
    Hello
    I'm working on a homework question and I am looking for some assistance.
    The question refers back to another, but I believe this is all the information below.

    n = 20
    variance = 1.4
    let S^2 denote the sample variance of the 20 measurements

    a) find b such that P(S^2 < b) = .975
    b) find a such that P(a < S^2) = .975

    the answers are given in the back, which are
    a) 2.42
    b) 0.656
    You need to know the distribution of the sample variance. Click on 6.1 at this link: Variance - Wikipedia, the free encyclopedia

    Post in this thread if you're still stuck (show you're working and say where you're stuck).
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  3. #3
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    ah thank you
    i figured it out.
    it may sound stupid, but i kept leaving out the important step of diving by the variance

    there was a part (c) i left out because those first two were priority in order to start this question.

    c) If a and b are as in parts (a) and (b), what is P(a < S^2 < b)?
    the answer is 0.95

    It is because both values cut off an area of 0.025 each, so together they would cut off 0.05, which 1-0.05=0.95?

    or is there a more complicated math to it?
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  4. #4
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    Quote Originally Posted by chrisc View Post
    ah thank you
    i figured it out.
    it may sound stupid, but i kept leaving out the important step of diving by the variance

    there was a part (c) i left out because those first two were priority in order to start this question.

    c) If a and b are as in parts (a) and (b), what is P(a < S^2 < b)?
    the answer is 0.95

    It is because both values cut off an area of 0.025 each, so together they would cut off 0.05, which 1-0.05=0.95?

    or is there a more complicated math to it?
    Yes. If you draw a rough sketch of the pdf and shade the required area the reason is obvious.
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