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# Week7 - Stat231 William Marshall Stat231 William Marshall...

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Stat231 William Marshall Stat231 William Marshall June 17, 2010

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Stat231 William Marshall Week 7 Goals: More Confidence intervals Prediction Intervals More Confidence intervals (CLT based)
Stat231 William Marshall Review Data: y 1 , y 2 , ..., y n Model: Y i = μ + R i , R i G (0 , σ ), R’s independent Estimators ˜ μ = ¯ Y ˜ σ = i ( Y i - ˜ μ ) 2 n - 1 Sampling distributions ˜ μ - μ σ G (0 , 1) , ( n - 1) ˜ σ 2 σ 2 χ 2 n - 1 Pivotal quantity ˜ μ - μ ˜ σ/ n t n - 1 Random Interval P ( - c t n - 1 c ) = 0 . 95 P μ - c ˜ σ/ n μ ˜ μ + c ˜ σ/ n ) = 0 . 95 95% Confidence Interval μ - c ˆ σ/ n , ˆ μ + c ˆ σ/ n )

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Stat231 William Marshall Example 12 In a marketing study, a company wants to study the effect of changing advertising \$ spent on local television on immediate sales of their product. The marketing department company selects 5 levels of advertising (thousands of \$ per week). They then decide to apply each level of spending to 5 communities across the country and measure the total sales (\$1000) in the following week within each community.
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