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Confidence Interval for Chi-Squared - read the quantile

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    1000 samples each of size n=121, where observations Xi ~ iid N ( m, sigma^2), for each sample we calculate Confidence Interval: I = [ 0.75 s^2, s^2 + s^2/4 ] where s^2=(1/(n-1))[tex]\Sigma[/tex](Xi-X bar)^2

    how many samples include the true value of sigma^2, ie 1000 * prob.

    2. Relevant equations

    we know that (n-1) s^2/sigma^2 ~ Chi-sqrd with (n-1) degrees of freedom

    3. The attempt at a solution

    so i started:

    P (0.75s^2 < sigma^2 < s^2 + s^2/4) = P (0.75 < sigma^2/s^2 < 5/4) =
    =P (0.75/(n-1) < sigma^2/(s^2(n-1)) < 1.25/(n-1)) =
    =P (1.25/(n-1) < (n-1)s^2/sigma^2 < 0.75/(n-1)) =
    =P (1.25/120 < Chi-sqrd with (n-1) df < 0.75/120) =
    =[tex]\chi[/tex] n-1 df (0.75/120) - [tex]\chi[/tex] n-1 df (1.25/120) =
    =[tex]\chi[/tex] n-1 df (0.00625) - [tex]\chi[/tex] n-1 df (0.0104167) ..... =
    =1 -[tex]\alpha[/tex]

    and now im stuck, since i am not sure if i am allowed to deduct them, and whether the numbers represent the quantiles of chi-squared, and if yes, i have a complications to find them in the table since was trying to get each separaetely and then get the p value for v=120 and then deduct but dont like it....

    how do i finish it now to get the probability...

    thank you, if any

  2. jcsd
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