Suppose $X_{1},...X_{n}$ are independently, identically distributed Bernoulli random quantities with parameter $k$.
Consider the hypothesis test:
$H_{0}: k = k_{0}$ vs $H_{1} : k = k_{1} \ \ $where $k_{1} \gt k_{0}$.
Suppose, using the Neyman-Pearson lemma, we obtain a critical region of the form $C^{*} \ = \ \left\{ (x_{1},...,x_{n} : \sum\limits_{i=1}^{n} x_{i} \geq c) \right\}$
where c is the critical value, to perform this test such that $P(\sum\limits_{i=1}^{n} x_{i} \geq c | H_{0} \ true) = \alpha$ and the sampling distribution of $\sum\limits_{i=1}^n X_{i}$ is $Bin(n,k)$
My question is, what are the implications (eg advantages) of using the Neyman-Pearson lemma to derive this critical region? I'm not really sure how to go about it so any help would be greatly appreciated.
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kjetil b halvorsen
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Sam
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Which parameter of the binomial is $k$? You've written the binomial using $(n,p)$... – jbowman Dec 04 '13 at 18:09
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Apologies, I've edited it now. – Sam Dec 04 '13 at 18:46
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I would have a look at http://en.wikipedia.org/wiki/Neyman%E2%80%93Pearson_lemma - the proof is quite informative too and I strongly recommend going through it. – queenbee Apr 14 '14 at 12:42