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Mathematical Statistics Xi~N(6,25) P[1.860 < 3(Xbar - 6]/S

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Let X1, X2, ..., X9 be a random sample from a normal distribution, Xi~N(6,25), and denote by Xbar and S^2 the sample mean and sample variance. Use the standard statistical table for normal distribution.



    2. Relevant equations

    E[S^2] = δ^2 = 25

    S^2 = (ƩXi^2 - nXbar^2)/(n-1)


    3. The attempt at a solution

    I have to find the probability and I want to move Xbar to one side. To do that, I need to find the value of S. I have no idea how to do this. I don't know how to use the sum. All I know is that n=9. I got a very complicated integral from using E[S^2]. How do I find S? Or what should I do if I can't?
     
  2. jcsd
  3. Feb 28, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Look up the "Student's t-distribution".

    RGV
     
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