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Problem 5. Let X1, . . . , X1.l be i.i.d samples from a Bernoulli(p) population. It is desired to test H0 :p = 0.59,

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Problem 5. Let X1, . . . , X1.l be i.i.d samples from a Bernoulli(p) population. It is desired to test H0 :p = 0.59, versus H1 : p = 0.45. (1) Derive the rejection region of the LRT. (2) Use the central limit theorem to determine, approximately, the sam- ple size needed so that type I error and type II error are both at most 0.01

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