In an experiment to compare six different fertilizers for tomatoes, 36 individually potted seedlings are to be used, 6 to receive each fertilizer. The tomato plants will be grown in a greenhouse, and the total yield of tomatoes will be observed for each plant. The experimenter has decided to use a randomized blocks design: The pots are to be arranged in six blocks of 6 plants each on the greenhouse bench. Two possible arrangements of the blocks are shown in the accompanying figure. One factor that affects tomato yield is temperature, which cannot be held exactly constant throughout the greenhouse. In fact, a temperature gradient across the bench is likely. Heat for the greenhouse is provided by a steam pipe that runs lengthwise under one edge of the bench, so the side of the bench near the steam pipe is likely to be warmer.
Arrangement I:

Arrangement II:

(a) Which arrangement of blocks (I or II) is better? Why?
(b) Prepare a randomized allocation of treatments to the pots within each block. (Refer to Example 11.6.4 as a guide; assume that the assignments of seedlings to pots and of pots to positions within the block have already been made.)
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