A horticulturist is interested in examining A horticulturist is interested in examining the yield potential of three A horticulturist is interested in examining the yield potential of three new varieties of asparagus. She designed a study to evaluate the three new varieties relative to the standard variety. There were 16 plots available on a large test field for the study, but the plots were not homogeneous in that there was a distinct sloping from north to south throughout the field. Also, a soil analysis revealed a discernible nitrogen gradient, which ran from west to east across the field. Therefore, the horticulturists decided to assign the varieties V1, V2, V3, and V4, with V1 being the standard variety, to the plots in a Latin square arrangement. The values for marketable yield per plot (in kg/ ha) are given in the following table. Note that there is a missing yield for variety V4 in row 4 and column 1. This was due to a problem that occurred during one of the harvesting ­periods.

a. Estimate the amount of marketable yield for variety V4 planted in a plot with ­nitrogen level N4 and slope S1.
b. Analyze the data by replacing the missing value with the estimate obtained in part (a), and then perform an analysis of variance using the formulas for a Latin square design with no missing observations.
c. Is there a significant difference in the mean marketable yields for the four varieties? Use α = 0.05.

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Sloping Nitrogen SI S2 S3 S4 N1 N2 N3 N4 V3 1,045.38 VI 82140 V2 1,004.02 V4 V1 807.69 V2 992.56 V41,091.23 V3 1090.97 V2 967.36 V4 992.47 V3 1,062.01 V1 893.32 V4 1,084.23 V3 1,029.53 V1 83653 V2 1,053.97