0
$\begingroup$

Let $X_1...X_n$ be idndependent and identically distributed as Bernoulli random quantities with parameter $p$. Let $p_1>p_0$ and consider the test of hypotheses $H_0:p=p_0$ versus $H_1:p=p_1$

Using the Neyman-Pearson lemma, a critical region of the form $C^* = \{(x_1,...,x_n): \sum_i_=_1 ^n x_i\ge c\}$ is obtained to perform this test where $c$ is the critical value chosen so that $P(\sum_i_=_i ^n X_i \ge c|H_0$ true)=$\alpha$ and the sampling distribution of $\sum_i_=_1^n X_i$ is $Bin (n,p)$ that is Binomial with $n$ trials and probability of success $p$.

Could you please explain to me in detail the properties of the test based on the critical region $C^*$ and in particular those derived as a consequence of using the Neyman-Pearson lemma??

$\endgroup$
0
$\begingroup$

it will be the uniformly most powerful test of your hypotheses. That is, for any given Type I error rate, the Neyman-Pearson test will minimize the Type II error rate.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.