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Unformatted text preview: 7.2 Comparing Two Means twosample problems are among the most commonly encountered in statistics compare control group and treatment group Twosample problems the goal of inference is to compare the responses in two groups each group is considered to be a sample from a distinct population the responses in each group are independent of those in the other group Notation used to describe the two populations: Population Variable Mean Standard deviation 1 x 1 1 1 2 x 2 2 2 Inference is based on two independent SRSs, one from each population. Population Sample size Sample mean Sample sd 1 n 1 x 1 s 1 2 n 2 x 2 s 2 We are interested in the difference 1 2 . The difference x 1  x 2 is a natural estimator. The mean and variance of x select an SRS of size n from a population and measure variable X on each individual in sample the n measurements are values of n random variables X 1 , X 2 X n if population is large relative to the size of the sample X 1 , X 2 X n considered independent X i is measurement on one individual selected at random from pop has the pop distribution x = n 1 ( X 1 + X 2 ++ X n ) 2 Twosample z statistic Suppose that x 1 is the mean of an SRS of size n 1 drawn from an N( 1 , 1 ) population and that x 2 is the mean of an SRS of size n 2 drawn from an N( 2 , 2 ) population. Then the twosample z statistic z = 2 2 2 1 2 1 2 1 2...
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 Spring '08
 ABDUS,S.

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