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April 16th, 2010, 08:03 AM  #1 
Newbie Joined: Apr 2010 Posts: 1 Thanks: 0  confidence interval chi squared
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/(n1))SIGMA(Xi  X bar)^2 how many samples include the true value of sigma^2, ie 1000 * prob. we know that (n1) s^2/sigma^2 ~ Chisqrd with (n1) degrees of freedom 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/(n1) < sigma^2/(s^2(n1)) < 1.25/(n1)) = =P (1.25/(n1) < (n1)s^2/sigma^2 < 0.75/(n1)) = =P (1.25/120 < Chisqrd with (n1) df < 0.75/120) = = chi n1 df (0.75/120)  chi n1 df (1.25/120) = = chi n1 df (0.00625)  chi n1 df (0.0104167) ..... = =1 alpha and now im stuck, i am not sure if i am allowed to deduct them, and whether the numbers represent the quantiles of chisquared, and if yes, i have a complications to find them in the table, was also thinking to get each separaetely 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 nicky 

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chi, confidence, interval, squared 
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