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Math Help - Interval Estimation

  1. #1
    Newbie
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    Smile Interval Estimation

    Q: A random sample of size 15 from a population which is n( μ, σ2 )
    yields
    =3.2 and S^2=4.24 Find 90% confidence interval for σ2.

    I know confidence interval for σ2 is [ns^2/b, ns^2/a]

    but how values to determine a and b??? in my book they have assign a=6.57 and b=23.7
    BUT HOW??? please tell .. i have to try another question of same type ...

    thanks .........!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Sameera View Post
    Q: A random sample of size 15 from a population which is n( μ, σ2 )
    yields
    =3.2 and S^2=4.24 Find 90% confidence interval for σ2.

    I know confidence interval for σ2 is [ns^2/b, ns^2/a]

    but how values to determine a and b??? in my book they have assign a=6.57 and b=23.7
    BUT HOW??? please tell .. i have to try another question of same type ...

    thanks .........!!
    ns^2 is the sum of the squares of 15 normally distributed RV's (almost as we are estimating the mean from the sample, so we in practice have one less degree of freedom). This has a \chi^2 distribution with \nu=14, and your values of a and b come from the \chi^2 tables. (your confidence interval is a 90\% interval)

    CB
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