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# Week9 - Stat231 William Marshall Stat231 William Marshall...

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Stat231 William Marshall Stat231 William Marshall June 29, 2010

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Stat231 William Marshall Week 9 Goals: Hypothesis testing in Gaussian models
Stat231 William Marshall Example 16 A car company advertises that a certain model uses 6.3 l/100km in city driving. A testing agency wants to examine this claim. Plan: Use a standard city driving test to measure the fuel consumption on 10 vehicles selected Data: 6.44, 6.52, 6.26, 6.21, 6.35, 6.56, 6.25, 6.39,6.58, 6.47 Model: Y i = μ + R i , R i G (0 , σ )

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Stat231 William Marshall Step 1 What does μ represent? What hypothesis would we like to test in the context of the problem? What is H 0 in the context of the probability model?
Stat231 William Marshall Step 2 What are the maximum likelihood estimates of ( μ, σ )? ˆ μ = 6 . 403 , ˆ σ = 0 . 133 What are the corresponding estimators? What is their sampling distribution?

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Stat231 William Marshall Step 3 Discrepancy measure D = | ˜ μ - μ 0 | ˜ σ/ n D=0 corresponds to the maximum agreement with the hypothesis Observed discrepancy d obs = | ˆ μ - μ 0 | ˆ σ/ n What is the sampling distribution of D?
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