Results 1 to 1 of 1

Math Help - findFinding a Uniformily Most Powerful Region

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    218

    Finding a Uniformily Most Powerful Region

    Let X_1,...,X_{25} be from a sample of 25 from a normal distribution N(\theta,100). Find a UMP region with \alpha = 0.1 for testing H_0:\theta=75 \ VS \ H_1:\theta>75

    So after performing the Likelihood ratio test, I determined the critial region to be (\Sigma X_i => K) where K is some constant.

    Using the CLT \frac{\Sigma X_i - n\mu}{\sigma \sqrt{n}}

    P(\Sigma X_i => K) =P_{H_0}( \frac{\Sigma X_i - 25(75)}{10\sqrt{75}} => \frac{K - 25(75)}{10\sqrt{75}} )=0.1

    \frac{K - 1875}{86.6}=1.28 solving for K = 1985.848

    Have I made a mistake anywhere?
    Last edited by statmajor; March 5th 2010 at 01:18 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The region 0 < x < y < z < 1
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 13th 2011, 09:08 AM
  2. centroid of region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 25th 2011, 12:46 AM
  3. need help to construct UMPT (uniformly most powerful test)
    Posted in the Advanced Statistics Forum
    Replies: 19
    Last Post: February 23rd 2011, 06:52 PM
  4. Replies: 0
    Last Post: April 18th 2010, 07:17 AM
  5. region
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 23rd 2008, 06:16 PM

Search Tags


/mathhelpforum @mathhelpforum