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A matched pairs experiment designed to study the response of people to a certain medication will be conducted using the following volunteers:

[tex]
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Subject} & \text{Gender} & \text{Age} & \text{Height (in)} & \text{Weight (lbs)} \\
\hline
A & F & 51 & 55 & 165 \\
B & F & 47 & 57 & 147 \\
C & M & 50 & 60 & 194 \\
D & F & 42 & 58 & 145 \\
E & M & 51 & 61 & 225 \\
F & M & 46 & 64 & 188 \\
\hline
\end{array}
\]
[/tex]

Which subjects should be blocked together to control for a response associated with a difference in gender?

A. A and C
B. A and D
C. C and D

Answer :

We need to block subjects so that the subjects in each pair have the same gender. This way, any differences in response due to gender are controlled for when comparing the medication effect.

Step 1. Identify the gender for each subject:

- Subject A is female.
- Subject C is male.
- Subject D is female.

Step 2. Analyze each option:

1. For the pair of subjects A and C:
- Since A is female and C is male, they are of different genders.

2. For the pair of subjects A and D:
- Both A and D are female. Thus, they are of the same gender.

3. For the pair of subjects C and D:
- C is male while D is female, so they are of different genders.

Since only the pair consisting of subjects A and D are the same gender, the optimal blocking to control for gender differences is:

[tex]$$\text{Subjects A and D.}$$[/tex]

Thus, the correct answer is the second option: A and D.

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