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# 7_2_Handout - 7.2 Comparing Two Means two-sample problems...

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7.2 Comparing Two Means two-sample problems are among the most commonly encountered in statistics compare control group and treatment group Two-sample 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 μ 1 σ 1 2 x 2 μ 2 σ 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 μ 1 – μ 2 . The difference x 1 - x 2 is a natural estimator.

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The mean and variance of x (recall from 5.2, page 1) 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 X i is measurement on one individual selected at random from pop- has the pop distribution if population is large relative to the size of the sample- X 1 , X 2 X n considered independent x = (1/n)( X 1 + X 2 +…+ X n ) EX 1 2
A fourth-grade class has 10 girls and 7 boys. The heights of 10-year-old girls are N(54.5, 2.7) and the heights of 10-year-old boys are N(54.1, 2.4). The heights of the students in our class are assumed to be random samples from these populations. What is the probability that the girls (X 1 ) are taller than the boys (X 2 ) on average?

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7_2_Handout - 7.2 Comparing Two Means two-sample problems...

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