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/(n-1))SIGMA(Xi - X bar)^2 how many samples include the true value of sigma^2, ie 1000 * prob. we know that (n-1) s^2/sigma^2 ~ Chi-sqrd with (n-1) 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/(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) = = chi n-1 df (0.75/120) - chi n-1 df (1.25/120) = = chi n-1 df (0.00625) - chi n-1 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 chi-squared, 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 Tags chi, confidence, interval, squared Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tay101 Advanced Statistics 1 January 7th, 2014 10:37 AM finalight Algebra 8 April 22nd, 2012 08:49 PM Kat-M Advanced Statistics 0 May 12th, 2009 11:21 AM shalomhk Advanced Statistics 1 August 1st, 2008 01:50 PM symmetry Advanced Statistics 1 June 18th, 2007 09:17 PM

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