2. Consider an incomplete block design with t=10 levels of the treatment factor.

(a) If a balanced incomplete block design (BIB) was constructed using the simplest method of forming blocks as all possible combinations of

????10 k

, how many blocks would be required for the cases where k=3, 4, 5, or 6?

(b) Using Equations (7.1) to (7.3), determine the minimum number of blocks that could possibly be required for a BIB with t=10, and k=3, 4, 5, or 6?

(c) Is it possible to nd a BIB with t=10, and k=3, 4, 5, or 6, by modifying the SAS code in Section 7.2?

(d) Can one or more generalized cyclic incomplete block design with t=10 and k=3 be found with less blocks than required for a BIB design? What number of blocks would be required for these designs? Using SAS proc plan as illustrated in Section 7.4, nd these designs.