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5. Suppose we are interested in the effect of two different kinds of potting soil on the number of days to germination of three varieties of carrot seed. The following table displays the data Soil 1 Variety 2 13 15 Variety 3 14 24 Variety 1 6 10 11 2 5 9 8 2 32 18 9 12 The mean square error from an effects model which includes the main effects for soil and variety along with the interaction effect is 52. Construct two orthogonal interaction contrasts. Estimate one of them using a 95% confidence interval. b. Using one observation per cell, construct the design matrix using sum-to-zero restrictions a.