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# 09_21_09 - STAT 409 Fall 2009 Examples for Two independent...

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STAT 409 Examples for 09/21/2009 Fall 2009 Two independent samples: X 1 , X 2 , … , X n 1 Y 1 , Y 2 , … , Y n 2 from population 1 from population 2 mean μ 1 , std. dev. σ 1 mean μ 2 , std. dev. σ 2 If n 1 and n 2 are large, or population 1 and population 2 are approximately normal, then ( Y X - is (approximately) normal with mean μ 1 μ 2 and standard deviation 2 2 2 1 2 1 n n σ σ + . A confidence interval for μ 1 μ 2 is ( 29 2 2 2 1 2 1 2 Y X n n z σ σ + α ± - . If σ 1 and σ 2 are unknown, use ( 29 2 2 2 1 2 1 2 Y X n s n s t + α ± - “Conservative” approach: the number of degrees of freedom = the smaller of n 1 – 1 and n 2 – 1. Welch’s T : the number of degrees of freedom = - + - + 2 2 2 2 2 2 1 2 1 1 2 2 2 2 1 2 1 1 1 1 1 n s n n s n n s n s If n 1 and n 2 are large, t α / 2 can be approximated by z α / 2 .

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09_21_09 - STAT 409 Fall 2009 Examples for Two independent...

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