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Let x1, X2, ...,X, be a random sample from a normal population with unknown mean µ and an unknown variance -². At a given significance level a, derive the generalized likelihood ratio test for а, Ho : o< 5 H1 : 0 > 5. versus Completely specify the test when a = 0.05 and n = 26. Does the power function of the test depend on the mean of the population: The following ^answers" have been proposed. (a) For a = 0.05 and n = 26 the test rejects Ho when E(X¡ – Xn)² > 941.25. The power function of the test indirectly depends on the population mean µ via s = (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)? > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean µ via 8 =%. (e) None of the above. - The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

Let x1, X2, ...,X, be a random sample from a normal population with unknown mean µ and an unknown variance -². At a given significance level a, derive the generalized likelihood ratio test for а, Ho : o< 5 H1 : 0 > 5. versus Completely specify the test when a = 0.05 and n = 26. Does the power function of the test depend on the mean of the population: The following ^answers" have been proposed. (a) For a = 0.05 and n = 26 the test rejects Ho when E(X¡ – Xn)² > 941.25. The power function of the test indirectly depends on the population mean µ via s = (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)? > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean µ via 8 =%. (e) None of the above. - The correct answer is (a) (b) (c) (d) (e) N/A (Select One)

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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Let x1, X2, ..., Xn be a random sample from a normal population with unknown mean u and an unknown variance o?. At a given significance level a, derive the generalized likelihood ratio test for Ho : o< 5 H1 : o > 5. versus Completely specify the test when a = population: 0.05 and n = 26. Does the power function of the test depend on the mean of the The following `answers" have been proposed. %3B 26 (a) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 941.25. The power function of the test indirectly depends on the population mean u via = 7. (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 26 ,26 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean u via 8 = . (e) None of the above. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)
Transcribed Image Text:Let x1, X2, ..., Xn be a random sample from a normal population with unknown mean u and an unknown variance o?. At a given significance level a, derive the generalized likelihood ratio test for Ho : o< 5 H1 : o > 5. versus Completely specify the test when a = population: 0.05 and n = 26. Does the power function of the test depend on the mean of the The following `answers" have been proposed. %3B 26 (a) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 941.25. The power function of the test indirectly depends on the population mean u via = 7. (b) For a = 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 941.25. The power function of the test does not depend on the population mean µ. (c) For a = 26 ,26 0.05 and n = 26 the test rejects Ho when E(X; – Xn)² > 188.25. The power function of the test does not depend on the population mean µ. (d) For a = 0.05 and n = 26 the test rejects Ho when E(X; – X„)² > 188.25. The power function of the test indirectly depends on the population mean u via 8 = . (e) None of the above. The correct answer is (a) (b) (c) (d) (e) N/A (Select One)
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