State the null hypotheses tested 4 f Explain what an interaction is 1 g Create

State the null hypotheses tested 4 f explain what an

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conclusions. State the null hypotheses tested. (4) (f) Explain what an interaction is. (1) (g) Create an interaction plot considering ONLY the two Insecticide levels 0 and 80, but ALL Herbicide levels. (2) (h) Using the above interaction plot, do Insecticide and Herbicide interact? If so, describe in words the effect on the dry weight of roots. (2) (i) Give an estimate of ( αβ ) 55 , i.e. the interaction effect at levels Herbicide = 2 and Insecticide = 80. (2) (j) Make suggestions for further analyses, i.e. how would you investigate the exact form of the relationship of Herbicide and Insecticide on the response? (2) [ 18 ] 5
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5. A fertilizer trial on a certain type of grass was conducted in a randomized complete block design by a management scientist. Five fertilizer treatments were randomly assigned to plots in each of five blocks. The response (summarised in the table below) is the amount of phosphorus in a plant tissue sample from each plot. Block Treatment 1 2 3 4 5 1. No fertilizer 7.6 8.1 7.3 7.9 9.4 2. 50 lb nitrogen 7.3 7.7 7.7 7.7 8.2 3. 100 lb nitrogen 6.9 6.0 5.6 7.4 7.0 4. 50 lb nitrogen + 75 lb P 2 O 5 10.8 11.2 9.0 12.9 11.6 5. 100 lb nitrogen + 75 lb P 2 O 5 9.6 9.3 12.0 10.6 10.4 Analysis of Variance Table: ----------------------------------------------- Df Sum Sq Mean Sq F value Pr(>F) treat 4 72.118 18.030 22.6048 2.036e-06 block 4 4.954 1.239 1.5529 0.2347 Residuals 16 12.762 0.798 ----------------------------------------------- (a) Write down a suitable linear model for this experiment, explaining all terms. (3) (b) Based on the analysis of variance table given above, what conclusions can be made about the effects of the treatments on phosphorus in plant tissue? Give a reason for your answer. (2) (c) Using the residual plots given below, comment on the validity of your above conclusions. (3) (d) Construct 95% confidence intervals for the following two contrasts: i. The effect of changing the nitrogen level. ii. The effect of adding P 2 O 5 . Give a clear interpretation of both confidence intervals. (6) (e) For this particular experiment, what may have been the reason for blocking? (1) (f) Briefly explain under which circumstances it would be appropriate to treat the blocks as random effects and when this would not be appropriate. (2) [ 17 ] 6
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-2 -1 0 1 2 -2 -1 0 1 2 3 theorectical quantiles Standardized residuals 23 18 19 6 7 8 9 10 11 -2 -1 0 1 2 3 fitted values standardized residuals 1 2 3 4 5 -2 -1 0 1 2 3 block standardized residuals 1 2 3 4 5 -2 -1 0 1 2 3 treatment standardized residuals 7
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6. A research engineer studied the time efficiency of four construction methods (A, B, C, D) for an electronic component. Four technicians were selected for the study.
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