Let Y1, Y2,..., Yn denote a random sample from a Bernoulli-distributed population with
Chapter 10, Problem 10.102(choose chapter or problem)
Let Y1, Y2,..., Yn denote a random sample from a Bernoulli-distributed population with parameter p. That is, p(yi | p) = pyi(1 p) 1yi, yi = 0, 1. a Suppose that we are interested in testing H0 : p = p0 versus Ha : p = pa , where p0 < pa . i Show that L(p0) L(pa ) = p0(1 pa ) (1 p0)pa yi 1 p0 1 pa n ii Argue that L(p0)/L(pa ) < k if and only if n i=1 yi > k for some constant k. iii Give the rejection region for the most powerful test of H0 versus Ha . b Recall that n i=1 Yi has a binomial distribution with parameters n and p. Indicate how to determine the values of any constants contained in the rejection region derived in part [a(iii)]. c Is the test derived in part (a) uniformly most powerful for testing H0 : p = p0 versus Ha : p > p0? Why or why not?
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