An experimenter wanted to determine how the gear selected on a 10 speed bike would aect the time it takes a rider to pedal up a long, gradual hill.

The experimental unit will be the trial or point in time when a rider will ride up the hill. Treatment will be the gear selected on the bicycle. Since the experimenter would like his conclusions to apply to all riders, he would like to run a blocked experiment where several riders (blocks) test each gear.

However, if each rider who participates in his study must test all gears in separate trials, he or she will become fatigued and variability in time to climb the hill will increase. Therefore, the experimenter decided to do an incomplete block design wherein each rider participating in his study will test only a subset of 4 of the 10 gears.

(a) If the experimenter were to use a balanced incomplete block (BIB) design by choosing all possible subsets of 4 selected from 10 as his blocks, how many riders or blocks would he need to recruit to his study?

(b) Using Equations (7.1){(7.3) or the BIBsize function in daewr, determine the minimum possible number of blocks that would be required for BIB design.

(c) Modify the R code in Section 7.2 to create a BIB with the number of blocks you found in

(b) using the optBlock function in the AlgDesign package.