An engineering professor wants to determine which subject engineering students find most difficult among statistics, physics, and chemistry. She obtains the final exam grades for four students who took all three courses last semester and who were in the same sections of each class. The results are presented in the following table.

Student Course 1 2 3 4 Statistics 82 94 78 70 Physics 75 70 81 83 Chemistry 93 82 80 70

a. The professor proposes a randomized complete block design, with the students as the blocks. Give a reason that this is likely not to be appropriate.

b. Describe the features of the data in the preceding table that suggest that the assumptions of the randomized complete block design are violated.