Pretend you have 4 designs that are being proposed for an experiment to evaluate a new teaching program (group T) against the existing teaching method (group C). The population consists of 12 schools, with 120 classes in each school and 2400 students in each school (20 students per class).

Design A: A simple random sample of 1200 children is selected across the 12 schools, and 600 children are randomly assigned to group T and 600 to group C.

Design B: In each of the 12 schools, 50 children are randomly assigned to group T, and 50 children are randomly assigned to group C.

Design C: In each of the 12 schools, 4 classes are selected randomly, and 2 classes are randomly assigned to group T and 2 to group C. Every student (20) in each class receives the same treatment.

Design D: Half of the schools (6) are assigned randomly to group T, and the other 6 schools are assigned to group C. In each school, 4 classes are selected randomly, and every student (20) in those selected classes in that school, receive the same treatment.

Required

a. What is the design characteristic of each design option (i.e. completely randomized, randomized block design, hierarchical design)?
b. Which design has the smallest expected variance (the best precision)?
c. Which design is best protected against contamination between the treatment and control