7.4. Four levels of fertilizer were used in a field experiment, with and without irrigation. The eight treatment combinations were assigned at random to eight plots. Barley yields were in bushels per acre. Level of Fertilizer Irrigation None Low Medium High No 317 341 354 329 Yes 275 304 334 380 (a) State the appropriate model. (b) Fill in an analysis of variance table. (c) Test whether fertilizers make any difference. (d) Estimate the overall difference in yield due to irrigation (point estimate and confidence interval estimate). (e) Estimate the mean difference in yield between no fertilizer and fertilizer at a low level (point estimate and confidence interval estimate).
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State the appropriate model: The appropriate model for this experiment is a two-way ANOVA model, with factors being the level of fertilizer and irrigation. The model can be written as: $Y_{ij} = \mu + \alpha_i + \beta_j + (\alpha\beta)_{ij} + Show more…
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Four kinds of fertilizer $f_{1}, f_{2}, f_{3},$ and $f_{4}$ are used to study the yield of beans. The soil is divided into 3 blocks, each containing 4 homogeneous plots. The yields in kilograms per plot and the corresponding treatments are as follows: Conduct an analysis of variance at the 0.05 level of significance using the randomized complete block model.
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