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# ***3 PART QUESTION*** Objective: The objective of this activity is

to examine differences among several experimental designs, particularly, single factor, multi-factor, and block designs. Topics covered: 1. Single factor designs 2. Multi-factor designs 3. Block designs Consider the following motivating example: 1. An agronomist wanted to compare the yield of three different varieties of rice (A, B, C). So, within a field, he randomly assigned each variety to five plots. The yield[s] in pounds per acre were recorded for each plot. (a)What is the response in the study? (b) What is the factor in the study? What are the factor levels? (c) What are the treatments? What are the blocks, if any? (d) What are the experimental units in the study? How many are there in total? (e) What is the name of the design of this experiment? (Single factor, two-factor, block) (f) Outline the design of the experiment.    2. Now, suppose that the agronomist is also interested in how a particular type of fertilizer, in addition to the variety, affects the mean rice yield. So, he randomly applies the combination of each variety and fertilizer (either the fertilizer is present or not present) to five plots in a field. Again, the yield[s] in pounds per acre were recorded for each plot. (a)What is the response in the study? (b) What are the factors in the study? What are the factor levels? (c) What are the treatments? What are the blocks, if any? (d) What are the experimental units in the study? How many are there in total? (e) What is the name of the design of this experiment? (Single factor, two-factor, block) (f) Outline the design of the experiment. 3. Go back to the original experiment in (1) where we are only interested in variety, not fertilizer. The agronomist realized that he wanted his results to apply over a range of soil conditions. So, he decided to conduct the experiment on 4 different locations (subdivisions) in a field so that the elevation and type of soil vary. He planted each variety on one plot within each subdivision of the field. Again, the yield[s] in pounds per acre were recorded for each plot. (a)What is the response in the study? (b) What is the factor in the study? What are the factor levels? (c) What are the treatments? What are the blocks, if any? (d) What are the experimental units in the study? How many are there in total? (e) What is the name of the design of this experiment? (Single factor, two-factor, block) (f) Outline the design of the experiment-please include images of the design

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