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 and80, 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 = 2and Insecticide = 80. (2)(j) Make suggestions for further analyses, i.e. how would you investigate the exactform of the relationship of Herbicide and Insecticide on the response? (2)[18]5
5. A fertilizer trial on a certain type of grass was conducted in a randomized completeblock design by a management scientist. Five fertilizer treatments were randomlyassigned to plots in each of five blocks.The response (summarised in the tablebelow) is the amount of phosphorus in a plant tissue sample from each plot.BlockTreatment123451. No fertilizer7.68.17.37.99.42. 50 lb nitrogen7.37.77.77.78.23. 100 lb nitrogen6.96.05.67.47.04. 50 lb nitrogen + 75 lb P2O510.811.29.012.911.65. 100 lb nitrogen + 75 lb P2O59.69.312.010.610.4Analysis of Variance Table:-----------------------------------------------Df Sum Sq Mean Sq F valuePr(>F)treat4 72.118 18.030 22.6048 2.036e-06block4 4.9541.239 1.55290.2347Residuals16 12.7620.798-----------------------------------------------(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 bemade about the effects of the treatments on phosphorus in plant tissue? Givea reason for your answer. (2)(c) Using the residual plots given below, comment on the validity of your aboveconclusions. (3)(d) Construct 95% confidence intervals for the following two contrasts:i. The effect of changing the nitrogen level.ii. The effect of adding P2O5.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 theblocks as random effects and when this would not be appropriate. (2)[17]6
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.