3. Consider an experiment to compare 7 treatments in blocks of size 5, with an anticipated error variance

of at most 30 squared units.

(a) [2pts] Verify that the following conditions cannot be satisfied with less than b = 21 blocks

vr = bk

r(k-1)= X(v - 1)

[Hint: For each b ≤ 20, calculate r and A according to the above formula. Show the b = 21 is the

minimum that yields both an integer r and an integer X. ]

(b) [3pts]Assuming that a balanced incomplete block design exists with b= 10 blocks and r = 6, and the

error variance is at most 30 squared units, calculate the width of 95% simultaneous confidence intervals

of a pairwise comparison using Tukey's method.

(c) [3pts]Repeat part (b) using Dunnett's method for treatment versus control comparisons.