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Let X have a Bernoulli distribution with pmff (x; p) =

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 8E Chapter 8.5

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 8E

PROBLEM 8E

Let X have a Bernoulli distribution with pmf

f (x; p) = px(1 − p)1−x, x = 0, 1, 0 ≤ p ≤ 1.

We would like to test the null hypothesis H0: p ≤ 0.4 against the alternative hypothesis H1: p > 0.4. For the test statistic, use where X1,X2, . . . ,Xn is a random sample of size n from this Bernoulli distribution. Let the critical region be of the form C = {y: y ≥ c}.

(a) Let n = 100. On the same set of axes, sketch the graphs of the power functions corresponding to the three critical regions, C1 = {y : y ≥ 40}, C2 = {y :y ≥ 50}, and C3 = {y : y ≥ 60}. Use the normal approximation to compute the probabilities.

(b) Let C = {y : y ≥ 0.45n}. On the same set of axes, sketch the graphs of the power functions corresponding to the three samples of sizes 10, 100, and 1000.

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Chapter 8.5, Problem 8E is Solved
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Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Let X have a Bernoulli distribution with pmff (x; p) =