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Math Help - Sampling Distribution

  1. #1
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    Sampling Distribution

    Hi.

    I'm having a little problem solving this one.

    Let X(bar) and S^2 denote the sample mean and sample variance in random sampling, sample size 20 from a N(10,80) distribution population. Calculate the probabilities of the following events.

    10<= X(bar) <= 12, S^2 <= 108.8

    Z= (X(bar)-10/(root(80/20))

    Since X(bar) ~ (u, sigma^2/n), 10-10/(root(80/20) <= Z <= 12-10 / (root(80/20)

    0 <= Z<= 1

    19S^2/80 <= 10.8*19/80 ~ Chi-square (19)

    Now how do I find the common area between the two events?

    Also how should I approach

    X(bar) <= 10 + 0.2037S


    Thanks.
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  2. #2
    MHF Contributor
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    Re: Sampling Distribution

    Hey rokman54.

    X_bar and S^2 should be independent so there will be nothing in common between the those two events. If there is then you can't use the common distributional assumptions (like a t-test for example).

    If X_bar and S^2 are dependent on each other than you should not have a Normal distribution (in relation to the same way that mu and sigma^2 are independent parameters).
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  3. #3
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    Re: Sampling Distribution

    Thanks.

    Also I figured out how to do the second : a simple t distribution.
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