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FinalExam514S2010

FinalExam514S2010 - Stat514S2010 Final Exam(Total 40 Points...

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Stat514S2010 Final Exam (Total 40 Points) 0. Exam time: two hours. 1. Use α = 5% throughout the exam. 2. Must show work to get credits. 3. Hand in both question and answer sheets. 1. An experiment was conducted by a biologist to study the effect of ethanol on sleep time. A sample of 16 rats was selected and each rate was given an oral injection of a particular concentration of ethanol per body weight. The group not injected ethanol (i.e. the concentration level is 0) was considered the control group. The rapid eye movement (REM) sleep time for each rat was then recorded for a 24-hour period. The data are given below. Concentration(g/kg) sleep time (min) Mean Std Dev 0 85.8, 78.4, 91.6, 94.2 87.500 7.010 1 63.2, 54.1, 69.4, 55.3 60.500 7.176 2 45.1, 60.7, 50.4, 56.5 53.175 6.846 3 31.2, 39.8, 45.5, 48.4 41.225 7.578 The grand mean is ¯ y .. = 60 . 6 and the total sum of squares is SS T = 5231 . 24. a)(2) Test if the ethanol concentration levels have different effects on sleep time. b)(2) Let Γ = - 3 μ 1 - μ 2 + μ 3 +3 μ 4 be the linear effect contrast of the four ethanol levels. Calculate the sum of squares due to Γ and test if it is significant. c)(2) Suppose the biologist was interested in comparing the three nonzero ethanol levels with the control in pairs. Calculate the critical difference for two levels to be different (i.e. CD) if Scheffe’s method is used.

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