L25posted

L25posted - Tests Comparing 1 with 2 Independent random...

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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 4.6-1 . 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.

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L25posted - Tests Comparing 1 with 2 Independent random...

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