# Were placed into each of 12 pens four blocks were

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were placed into each of 12 pens. Four blocks were formed from groups of 3 pens based on location”. There are 6*3=18 experimental units in each block. There are in total 12 different experimental units in this study. b) Only treatment O is significant in the linear model. c) c) Yes, the treatment is significant. d) e)　From the TukeyHSD testing, we see that treatment E and F are not significant. Treatment O seems different from E and F. However, we cannot reject treatment O at 0.05 level but it is fairly close to 0.05. If 0.05 is used as p value, no pairs are significant. Problem3 a) Shade and irrigation are two blocking factors.
STAT425-HW6 Yue Wang , yuewang3, graduate 4 credit b) Shade irrigation 1 2 3 4 5 1 A D C E B 2 B E D A C 3 C B A C E 4 D A E B D 5 E C B D A c) d) e) > TukeyHSD(aov(yield~shade+irrigation+inoculum))\$inoculum diff lwr upr p adj B-A -0.72 -4.250202 2.810202 0.9633432745 C-A -0.08 -3.610202 3.450202 0.9999928279 D-A -0.86 -4.390202 2.670202 0.9326392350 E-A -6.60 -10.130202 -3.069798 0.0005166455 C-B 0.64 -2.890202 4.170202 0.9759058775 D-B -0.14 -3.670202 3.390202 0.9999331812 E-B -5.88 -9.410202 -2.349798 0.0014163428 D-C -0.78 -4.310202 2.750202 0.9515868499 E-C -6.52 -10.050202 -2.989798 0.0005764154 E-D -5.74 -9.270202 -2.209798 0.0017334480 f) The only four pairs that have significant difference are A-E,B-E,C-E,D-E. Because E is the control. However, inoculum A,B,C,D seems to be no difference among them. Prob 4 a) football<-read.table("football.txt",header=TRUE) Summary is displayed below.
STAT425-HW6 Yue Wang , yuewang3, graduate 4 credit b) The proper test in this case would be a paired t-test.
d)
STAT425-HW6 Yue Wang , yuewang3, graduate 4 credit