FinalExam514F2010

# FinalExam514F2010 - Stat514F2010 Final Exam (Total 40...

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Stat514F2010 Final Exam (Total 40 Points) 1. Exam time: two hours and ten minutes 2. Use α =5% throughout the exam. 3. Must show work to get credits. 4. Hand in both question and answer sheets. 1. To study the eﬀect of a certain type of gasoline additive on automobile emission, an experiment involving ﬁve drivers, ﬁve cars, and ﬁve levels of the additive is performed. The ﬁve levels of the additive are 5, 10, 15, 20, and 25 units per gallon gasoline, denoted by A , B , C , D ,and E , respectively. The response is the amount of emission an automobile produces over a period of time. The data generated from the experiment are given below. Driver C a r 12345 1 A =53 B =23 C =43 D =37 E =54 2 B =48 C =20 D =42 E =34 A =47 3 C =40 D =9 E =38 A =28 B =33 4 D =36 E =18 A =39 B =26 C =27 5 E =46 A =25 B =32 C =22 D The grand mean is ¯ y .. . 16 and the level means of the additive are A: xxx B: 32.4 C: 30.4 D: 31.6 E: 38.0 Part of the ANOVA table generated by SAS is given below. Source DF Sum Squares Mean Square F Value Pr > F Model 12 2958.480000 246.540000 24.08 <.0001 Error 12 122.880000 10.24000 Cor Total 24 3081.360000 car 4 643.760000 160.940000 15.72 0.0001 driver x xxx xxx xxx xxx additive x xxx xxx xxx xxx Suppose the statistical model y ijk = μ + α i + τ j + β k + ² ijk for 1 i, j, k 5 is used to analyze the data, in which α i , τ j β k are the eﬀects of cars, additive levels, and drivers, respectively, which are further subject to the zero-sum constraints. a)(2pts) Obtain the estimates of τ j ’s. b)(2pts) Test if the levels of the additive have diﬀerent impact on automobile emission.

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## This note was uploaded on 12/09/2011 for the course STAT 514 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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FinalExam514F2010 - Stat514F2010 Final Exam (Total 40...

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