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1. An investigator is interested in determining which factors affect germination rate in a new variety of cilantro seed. Five factors (A: amount of light per day, B: soil type, C: amount of water per day, D: temperature, and E: mulch type), each with two levels, are considered. An experiment with a 2"- fractional factorial design is performed. Briefly, 16 large planters are randomly assigned to the treatments listed in the first column in the table on the left below. In each pot, 100 randomly selected cilantro seeds are planted (in the assigned soil type) and subjected to the assigned conditions of its treatment for 14 days. After 14 days, the number of seeds that germinated is determined for each pot. Below, two tables are provided. In the table on the left, the first column provides the treatments and the second column provides the number of seeds that germinated. The table on the right provides the estimates and sums of squares for some of the effects in this experiment. Treatment Observation Effect Estimate SS (1 ) 67 A 11.75 552.25 43 B 15.25 930.25 be 41 C -2.00 16.00 ab 61 D ce 67 E 0.50 1.00 ac 44 AB 12.25 20.25 bc 37 AC 0.00 0.00 abce 58 AD 13.25 702.25 de 71 AE -1.50 9.00 ad 93 BC -0.50 1.00 42 BD abde 71 BE 0.50 1.00 67 CD acde 90 CE 9.75 380.25 bode 42 DE 0.50 1.00 abcd 68 a. Determine the defining relation for the design of this experiment. b. What is the resolution of this design? Justify your answer. c. Determine all pairs of aliases in this design. d. Determine the estimates missing in the table above (confounded with the effects of their aliases) e. Determine the sums of squares missing in the table above (confounded with the sums of squares of their aliases)