Question

15 multiple choice 3 points
(03.01 lc)
for a certain experiment, the available experimental units are six people: three females (f) and three males (m). use {1f, 2f, 3f} to denote the females and {1m, 2m, 3m} to denote the males. there are to be three treatment groups: a, b, and c. if a randomized block design is used, with the experimental units blocked by gender, which assignment of treatments is not correct?
a: {1f, 1m}, b: {2f, 2m}, c: {3f, 3m}
a: {2f, 1m}, b: {3f, 2m}, c: {1f, 3m}
a: {2f, 3m}, b: {3f, 2m}, c: {1f, 1m}
a: {1f, 2m}, b: {3f, 2f}, c: {3m, 1m}
a: {1f, 2m}, b: {2f, 1m}, c: {3f, 3m}

Explanation:

In a randomized block design blocked by gender, each block (gender group: females and males) should have one experimental unit per treatment group. There are 3 females (1f, 2f, 3f) and 3 males (1m, 2m, 3m), and 3 treatment groups (A, B, C). So each treatment group should have 1 female and 1 male (since total per treatment: 2 units, 1 from each block). Let's analyze each option:

• Option A: A: (1f, 1m), B: (2f, 2m), C: (3f, 3m) – Each group has 1f and 1m. Correct.
• Option B: A: (2f, 1m), B: (3f, 2m), C: (1f, 3m) – Each group has 1f and 1m. Correct.
• Option C: A: (2f, 3m), B: (3f, 2m), C: (1f, 1m) – Each group has 1f and 1m. Correct.
• Option D: A: (1f, 2m), B: (3f, 2f), C: (3m, 1m) – Group B has two females (3f, 2f) and no male, while group A and C have 1f and 1m (A:1f,2m; C:3m,1m – wait, C has two males? Wait, no: A:1f,2m (1f,1m? No, 2m is male. Wait, B: 3f (female) and 2f (female) – so B has 2 females, 0 males. The blocks are gender, so each treatment group must have one from each block (gender). So B has two from female block, zero from male block. Incorrect. Wait, the last option (let's check the options again, the fifth option: A: (1f, 2m), B: (2f, 1m), C: (3f, 3m) – each has 1f and 1m. Correct. Wait, the fourth option is A: (1f, 2m), B: (3f, 2f), C: (3m, 1m). Here, group B has two females (3f, 2f) – so no male in B, and group C has two males (3m, 1m) – no female in C. So this violates the block design (each treatment should have one from each block). So this assignment is NOT correct. Wait, let's recheck the options:

Wait the options are:

1. A: (1f, 1m); B: (2f, 2m); C: (3f, 3m) – correct.

1. A: (2f, 1m); B: (3f, 2m); C: (1f, 3m) – correct.

1. A: (2f, 3m); B: (3f, 2m); C: (1f, 1m) – correct (1f,1m; 3f,2m; 2f,3m – each 1f,1m).

1. A: (1f, 2m); B: (3f, 2f); C: (3m, 1m) – B has 3f (female) and 2f (female) – two females, no male. C has 3m (male) and 1m (male) – two males, no female. So this is incorrect because each treatment group must have one from each block (gender). So this assignment is NOT correct.

Wait, the options as given: the fourth option is "A: (1f, 2m), B: (3f, 2f), C: (3m, 1m)". Let's confirm:

• Block 1: Females (1f,2f,3f), Block 2: Males (1m,2m,3m). Each treatment group (A,B,C) should have 1 from Block 1 (female) and 1 from Block 2 (male).

In option D (the fourth option):

• Group A: 1f (Block1), 2m (Block2) – good (1 from each block).
• Group B: 3f (Block1), 2f (Block1) – two from Block1, 0 from Block2 – violates the block design (each group must have one from each block).
• Group C: 3m (Block2), 1m (Block2) – two from Block2, 0 from Block1 – violates.

So the incorrect assignment is the fourth option: A: (1f, 2m), B: (3f, 2f), C: (3m, 1m) (the option labeled as the fourth one, let's check the original options:

The options are:

1. A: (1f, 1m); B: (2f, 2m); C: (3f, 3m)

1. A: (2f, 1m); B: (3f, 2m); C: (1f, 3m)

1. A: (2f, 3m); B: (3f, 2m); C: (1f, 1m)

1. A: (1f, 2m); B: (3f, 2f); C: (3m, 1m)

1. A: (1f, 2m); B: (2f, 1m); C: (3f, 3m)

So the fourth option (A: (1f, 2m), B: (3f, 2f), C: (3m, 1m)) is incorrect because it has groups with two from one block and zero from the other, violating the randomized block design with gender blocks (each group needs one female and one male).

Answer:

A: (1f, 2m), B: (3f, 2f), C: (3m, 1m) (the fourth option in the list, as per the given choices: the option where B has two females and C has two males, and B has no male, C has no female)