An agricultural trial compares three fertilizer formulas (X, Y, Z) with n = 8 plots per formula. The ANOVA rejects the overall null. The instructor provides qcrit = 3.40 for alpha = 0.05, k = 3 groups, and df = 21. Use MSE = 9.0 and group means X = 12, Y = 15, Z = 20. Compute all three pairwise q statistics and state which pairwise comparisons are significant at alpha = 0.05.

• A. q_XY ≈ 2.83 (not significant), q_YZ ≈ 4.72 (significant), q_XZ ≈ 7.55 (significant); conclude Y vs Z and X vs Z differ.
• B. None of the q statistics exceed qcrit = 3.40, so fail to reject all pairwise null hypotheses and conclude the fertilizers perform equivalently across plots.
• C. q_XY ≈ 3.40 (borderline), q_YZ ≈ 4.00 (significant), q_XZ ≈ 6.00 (significant); conclude all three are significant at alpha 0.05.
• D. All pairwise q values exceed qcrit = 3.40 because the largest difference is large, therefore X differs from both Y and Z and Y differs from Z as well.

Answer: (A)