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Thread: 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 .........!!
    $\displaystyle ns^2$ is the sum of the squares of $\displaystyle 15$ 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 $\displaystyle \chi^2$ distribution with $\displaystyle \nu=14$, and your values of $\displaystyle a$ and $\displaystyle b$ come from the $\displaystyle \chi^2$ tables. (your confidence interval is a $\displaystyle 90\%$ interval)

    CB
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