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Let X1, X2, ... , Xn be a random sample of Bernoulli trials b(1, p). (a) Show that a
Chapter 8, Problem 8.6-4(choose chapter or problem)
Let X1, X2, ... , Xn be a random sample of Bernoulli trials b(1, p). (a) Show that a best critical region for testing H0: p = 0.9 against H1: p = 0.8 can be based on the statistic Y = n i = 1 Xi, which is b(n, p). (b) If C = {(x1, x2, ... , xn) : n i = 1 xi n(0.85)} and Y = n i = 1 Xi, find the value of n such that = P[ Y n(0.85); p = 0.9 ] 0.10. Hint: Use the normal approximation for the binomial distribution. (c) What is the approximate value of = P[ Y > n(0.85); p = 0.8 ] for the test given in part (b)?(d) Is the test of part (b) a uniformly most powerful test when the alternative hypothesis is H1: p < 0.9?
Questions & Answers
QUESTION:
Let X1, X2, ... , Xn be a random sample of Bernoulli trials b(1, p). (a) Show that a best critical region for testing H0: p = 0.9 against H1: p = 0.8 can be based on the statistic Y = n i = 1 Xi, which is b(n, p). (b) If C = {(x1, x2, ... , xn) : n i = 1 xi n(0.85)} and Y = n i = 1 Xi, find the value of n such that = P[ Y n(0.85); p = 0.9 ] 0.10. Hint: Use the normal approximation for the binomial distribution. (c) What is the approximate value of = P[ Y > n(0.85); p = 0.8 ] for the test given in part (b)?(d) Is the test of part (b) a uniformly most powerful test when the alternative hypothesis is H1: p < 0.9?
ANSWER:Step 1 of 4
Given:
