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This is a follow-up question to Question 4(a-c) in Homework 4. You don't have to corre answer that question in order to solve this question. Suppose X1,..., Xn " Bernoulli(p) with unknown p. Consider testing for Ho : p = vs. H1 : p+ Po for some known quantity po E (0, 1). Based on Question 4(c) in Homew 4, an approximate (1– a) x 100% CI for p (when n is large) is i.i.d. n- (1

This is a follow-up question to Question 4(a-c) in Homework 4. You don't have to corre answer that question in order to solve this question. Suppose X1,..., Xn " Bernoulli(p) with unknown p. Consider testing for Ho : p = vs. H1 : p+ Po for some known quantity po E (0, 1). Based on Question 4(c) in Homew 4, an approximate (1– a) x 100% CI for p (when n is large) is i.i.d. n- (1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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This is a follow-up question to Question 4(a-c) in Homework 4. You don't have to correctly answer that question in order to solve this question. Suppose X1, ... , Xn Bernoulli(p) with unknown p. Consider testing for Ho : p = Po vs. H1 : p + po for some known quantity po E (0, 1). Based on Question 4(c) in Homework 4, an approximate (1– a) x 100% CI for p (when n is large) is i.i.d. Pn+ Za/2\/ Pn(1 – Pn) Pn (1 – Pn) , În + %1-a/2\/ where Pn = X, and za is the B-quantile for standard normal. Please construct a hypothesis test with type I error rate being approximately 0.05 when n is large. Instruction: In your answer, please specify your test (i.e., when do you reject Ho and when do you not reject H?), and justify that it indeed has type I error rate 0.05. In your justification, if you cite a theorem studied in class, please name that theorem or state the slide number and lecture note number that contains the theorem. OUC at120B.
Transcribed Image Text:This is a follow-up question to Question 4(a-c) in Homework 4. You don't have to correctly answer that question in order to solve this question. Suppose X1, ... , Xn Bernoulli(p) with unknown p. Consider testing for Ho : p = Po vs. H1 : p + po for some known quantity po E (0, 1). Based on Question 4(c) in Homework 4, an approximate (1– a) x 100% CI for p (when n is large) is i.i.d. Pn+ Za/2\/ Pn(1 – Pn) Pn (1 – Pn) , În + %1-a/2\/ where Pn = X, and za is the B-quantile for standard normal. Please construct a hypothesis test with type I error rate being approximately 0.05 when n is large. Instruction: In your answer, please specify your test (i.e., when do you reject Ho and when do you not reject H?), and justify that it indeed has type I error rate 0.05. In your justification, if you cite a theorem studied in class, please name that theorem or state the slide number and lecture note number that contains the theorem. OUC at120B.
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