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Midterm222F2010

Midterm222F2010 - Stat514F10 Midterm II(Total 20 Points 0...

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Stat514F10 Midterm II (Total 20 Points) 0. Exam time: 2 hours ; 1. Use α = 5% throughout the exam ; 2. Must show work to get credits 3. Hand in both the question and answer sheets. 1. An experiment is conducted to study the performances of four different methods (denoted by A , B , C , and, D ) in measuring the presence of a certain contaminant in groundwater. Samples of groundwater from four different toxic-waste sites are collected and the four methods are used to measure the amount of the contaminant in these samples. The results are given below. Sites Methods 1 2 3 4 ¯ y i. A 23.8 7.6 15.5 30.6 19.375 B 19.2 6.8 13.2 22.5 15.425 C 20.9 5.9 14.0 27.1 16.975 D 24.5 8.1 16.2 32.0 20.200 ¯ y .j 22.1 7.1 14.725 28.05 17.994 Suppose the following statistical model is used to analyze the data, y ij = μ + τ i + β j + ij , where τ i (1 i 4) and β j (1 j 4) are the effects of the methods and sites, respectively, which satisfy the zero-sum constraints τ i = β j = 0. The total sum of squares is SST = 1070 . 109 . a)(2pts) Test if the four measurement methods differ in their performances.

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