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Unformatted text preview: Tests Comparing 1 with 2 Independent random samples { X 1 ,...,X n 1 } and { Y 1 ,...,Y n 2 } from N ( 1 , 2 1 ) ,N ( 2 , 2 2 ) popula tions respectively. Null hypothesis is: H : 1 = 2 If 2 1 , 2 2 known then test based on normal stan dardized score Z = If 2 1 , 2 2 not known but sample sizes large then use approximate normal standardized score Z = 1 Example 4.61 . Test H : 1 = 2 versus 1 > 2 As for testing a single mean where = , here = 1 2 and the estimator is = X Y . The null value of = 0 because 1 = 2 . So reject H if X Y is so large that the standardized score Z > z , equivalently X Y > = 2 . 84 z 2 OC curve Continue previous example. How good is this test when 6 = 0? OC ( ) = P (accept H  ) = P ( X Y < 2 . 84 z ) = P ( X Y 2 . 84 < 2 . 84 z  2 . 84 ) = P ( Z < z  2 . 84 ) = ( z  2 . 84 ) 3 Suppose = 0 . 25 so z = 1 . 96 .....
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This note was uploaded on 01/03/2012 for the course EE 1244 taught by Professor Drera during the Fall '10 term at Conestoga.
 Fall '10
 drera

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