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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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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