Question

For a certain experiment, the available experimental units are eight rats, of which four are female (F1, F2, F3, F4) and four are male (M1, M2, M3, M4). There are to be four treatment groups, A, B, C, and D. If a randomized block design is used, with the experimental units blocked by gender, which of the following assignments of treatments is impossible?

a.$A\to (F1,M1),B\to (F2,M2),C\to (F3,M3),D\to (F4,M4)$

b.$A\to (F1,M2),B\to (F2,M3),C\to (F3,M4),D\to (F4,M1)$

c.$A\to (F1,M2),B\to (F3,F2),C\to (F4,M1),D\to (M3,M4)$

d.$A\to (F4,M1),B\to (F2,M3),C\to (F3,M2),D\to (F1,M4)$

e.$A\to (F4,M1),B\to (F1,M4),C\to (F3,M2),D\to (F2,M3)$

Short answer

Option (c) A → (F1, M2), B → (F3, F2), C → (F4, M1), D → (M3, M4) assignments of treatment is impossible.

Step-by-step solution

Given Information

We have been given that the eight rats are provided for a certain experiment, four of which are female (F1, F2, F3, F4) and four of which are male (F1, F2, F3, F4) (M1, M2, M3, M4). And, A, B, C, and D are the four treatment groups that will be used.

Explanation

It is impossible for a treatment group to have two of the same gender. And, in option c, the D group has two of the same gender.

So, option (c) $A\to (F1,M2),B\to (F3,F2),C\to (F4,M1),D\to (M3,M4)$is the correct answer.