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Hi all I have a question about Hypothesis test, could you please help me?

If $X_{1},X_{2},\ldots,X_{n}$ are independent, where $X_{i}$ is $N(\theta_{i},1)$ , find the critical region and power function for the Most Powerful test of size $\alpha$ of

$H_{0}:\theta_{1}=\cdots=\theta_{n}=0$ against $H_{1}:\theta_{1}=\cdots=\theta_{r}=\frac{1}{2} , \theta_{r+1}=\cdots=\theta_{n}=-\frac{1}{2}$

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What does your book say about this? –  Dilip Sarwate Dec 12 '11 at 17:58
    
@DilipSarwate It is a question in the problem sheet. –  John Dec 12 '11 at 18:09
    
What do you know about Most Powerful tests? Surely your book mentions them –  deinst Dec 12 '11 at 20:48
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