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slide10 - Chapter 10 Estimation and Hypothesis Testing Two...

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Chapter 10: Estimation and Hypothesis Testing: Two Populations Bin Wang [email protected] Department of Mathematics and Statistics University of South Alabama Mann E6 1/37
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Parameter(s) of interests The differences between the two population means: μ 1 - μ 2 . Mann E6 2/37
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Parameter(s) of interests The differences between the two population means: μ 1 - μ 2 . What are we going to do? Or, what will you be required to do? Or what will be tested? Mann E6 2/37
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Parameter(s) of interests The differences between the two population means: μ 1 - μ 2 . What are we going to do? Or, what will you be required to do? Or what will be tested? 1 Find a (1 - α )100% confidence interval for μ 1 - μ 2 . Mann E6 2/37
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Parameter(s) of interests The differences between the two population means: μ 1 - μ 2 . What are we going to do? Or, what will you be required to do? Or what will be tested? 1 Find a (1 - α )100% confidence interval for μ 1 - μ 2 . 2 Test a hypothesis about μ 1 - μ 2 . Mann E6 2/37
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Notations Suppose we select two samples from two different populations that are referred to population 1 and population 2. Let μ 1 = the mean of population 1, μ 2 = the mean of population 2, σ 1 = the standard deviation of population 1, σ 2 = the standard deviation of population 2, n 1 = the size of sample drawn from population 1, n 2 = the size of sample drawn from population 2, ¯ x 1 = the mean of sample drawn from population 1, ¯ x 2 = the mean of sample drawn from population 2, s 1 = the standard deviation of sample 1, s 2 = the standard deviation of sample 2, Mann E6 3/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 . Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 . 1 What is the mean of ¯ x 1 - ¯ x 2 ? Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 . 1 What is the mean of ¯ x 1 - ¯ x 2 ? μ ¯ x 1 - ¯ x 2 = μ ¯ x 1 - μ ¯ x 1 = μ 1 - μ 2 Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 . 1 What is the mean of ¯ x 1 - ¯ x 2 ? μ ¯ x 1 - ¯ x 2 = μ ¯ x 1 - μ ¯ x 1 = μ 1 - μ 2 2 What is the standard deviation of ¯ x 1 - ¯ x 2 : Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 . 1 What is the mean of ¯ x 1 - ¯ x 2 ? μ ¯ x 1 - ¯ x 2 = μ ¯ x 1 - μ ¯ x 1 = μ 1 - μ 2 2 What is the standard deviation of ¯ x 1 - ¯ x 2 : σ ¯ x 1 - ¯ x 2 ? Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 . 1 What is the mean of ¯ x 1 - ¯ x 2 ? μ ¯ x 1 - ¯ x 2 = μ ¯ x 1 - μ ¯ x 1 = μ 1 - μ 2 2 What is the standard deviation of ¯ x 1 - ¯ x 2 : σ ¯ x 1 - ¯ x 2 ? 3 Hypothesis Testing Mann E6 4/37
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Point estimator Can you find a point estimator for μ 1 - μ 2 ? ¯ x 1 - ¯ x 2 .
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