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HW4_solution - Problem 1(a(b Its a paired t-test According...

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Problem 1 (a)(b) It s a paired t-test. According to (3.1), we can get: t = -3.08, p = 0.027 Since t 5, 0.05/2 = 2.571 < |t|, we reject the null hypothesis R code: > x1=c(8,14,16,19,18,12) > x2=c(11,16,20,18,20,15) > N=length(x1) > d = x1-x2 > s_d=sd(d) > t=sqrt(N)*mean(d)/s_d > t [1] -3.081296 > t.test(x1,x2,paired=TRUE) Paired t-test data: x1 and x2 t = -3.0813, df = 5, p-value = 0.02743 Problem 2 Zero sum: τ i is the offset between the expected treatment i response and the average treatment response. α i is the offset between the expected block j effect and the average block effect. Baseline: τ i is the offset between the expected treatment i response and treatment 1. α i is the offset between the expected block j effect and the block 1 effect. Problem 3 For tukey s method, we have: 1/sqrt(2) *q 4,24,0.01 = 3.47 The t-values are in table 3.7 We can see all pairs except A vs C have t-value greater than 3.47. The conclusion is different from the one made at 0.05 level Problem 4 >y=c(25.66,29.15,35.73,28.00,35.09,39.56,20.65,29.79,35.66) > X=rep(c(40,50,60),3) > p1=((X-50)/10)/sqrt(2) > p2=(3*(((X-50)/10)^2-2/3))/sqrt(6) > X2=rep(c(0,1,2),each=3) > s1=((X2-1)/1)/sqrt(2) > s2=(3*(((X2-1)/1)^2-2/3))/sqrt(6) >
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