2 (11 points) In the study to compare the three fertilizers and the two levels o

Question

2 (11 points) In the study to compare the three fertilizers and the two levels of watering on the
yield per bushel for a variety of corn, suppose the mean yields for each combination of fertilizer
(FA, FB, or FC) and watering level (WA or WB) are given in the following table:
              FA             FB                FC

WA      µ11 = 8    µ12 = 13   µ13 = 12

WB   µ21 = 10   µ22 = 12   µ23 = 11

1. (2 points) Is this an additive design? Justify your answer..
2. (3 points) Compute the main watering effects and the fertilizer effect. (You may also write your
answers at the margins of the table

1 = 2 = , 1 = , 2 = , 3 =
3. (3 points) Compute the interaction effects 11 and 12.
11 =                                  12 =
4. (3 points) Use the fact that the interaction effects in each row sum to zero, and similarly the
interaction effects in each column sum to zero to compute the remaining interaction effects.

13 =               21 =                  22 =                 23 =

Explanation / Answer

1. Is this an additive design? Justify your answer

. ANSWER: No because µ12 µ11 = 5 while µ22 µ21 = 2.
2. Compute the main watering eects and the fertilizer eect. (You may also write your answers at the margins of the table.)

ANSWER: 1 = 2 = 0, 1 = 2, 2 = 1.5, 3 = 0.5

3ans ) Compute the interaction eects. ANSWER: 11 = 1, 13 = 0.5,

4 ans ) 13 = 0.5, 21 = 1, 22 = 0.5, 23 = 0.5

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