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# class03_17 - 1.017/1.010 Class 17 Testing Hypotheses about...

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Unformatted text preview: 1.017/1.010 Class 17 Testing Hypotheses about Two Populations Tests of differences between two populations To test if two populations x and y are different we can compare specified distributional properties a x and a y (means, variances, 90 percentiles, etc.). Null hypothesis: H0 : a x = a y = a or a x- a y = 0 The hypothesis test may be based on "natural" (unbiased and consistent) estimators of a x and a y , derived from the independent random samples x 1 , x 2 ,..., x Nx and y 1 , y 2 ,..., y Ny : ) ,..., , ( ˆ ˆ 2 1 Nx x x x x x a a = ) ,..., , ( ˆ ˆ 2 1 Ny y y x x x a a = We can derive a two-sided rejection region R a 0 written in terms of a standardized statistic z , following the same basic procedure as in the single population case (see Class 15): ] ˆ- ˆ [ ) ˆ- ˆ ( ) , , ˆ , ˆ ( ] ˆ- ˆ [ ) ( ) ˆ- ˆ ( ) , , ˆ , ˆ ( y x y x y x y x y x y x y x y x SD a a SD a a a a a a a a a a z a a a a a a z = − − = ) 2- (1 ) , , ˆ , ˆ ( ) 2 ( ) , , ˆ , ˆ ( : 1 1 α α- z-...
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class03_17 - 1.017/1.010 Class 17 Testing Hypotheses about...

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