cse63146
Mar5-10, 04:18 PM
1. The problem statement, all variables and given/known data
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
2. Relevant equations
3. The attempt at a solution
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?
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
2. Relevant equations
3. The attempt at a solution
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?