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# 09_21_09ans - STAT 409 Fall 2009 Examples for Two...

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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 ( 29 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”: the number of degrees of freedom = the smaller of n 1 – 1 and n 2 – 1. Welch’s T : degrees of freedom = - + - + 1 1 1 1 2 2 2 2 2 2 1 2 1 1 2 2 2 2 1 2 1 n n n n n n s s s s If n 1 and n 2 are large, t α / 2 can be approximated by z α / 2 . 1. A new method of storing snap beans is believed to retain more ascorbic acid than the old method. In an experiment, snap beans were harvested under uniform conditions and frozen in 250 equal-size packages. One hundred of those packages were randomly selected and stored according to the new method, and the other 150

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09_21_09ans - STAT 409 Fall 2009 Examples for Two...

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