Sure! Let's break this down step-by-step:
1. Understanding the factorial design:
- Dr. Stephens is using a 2 x 3 factorial design.
- This implies that there are 2 levels for one factor and 3 levels for another factor.
- As a result, the total number of different conditions or cells in this design is [tex]\(2 \times 3 = 6\)[/tex].
2. Number of participants per cell:
- Dr. Stephens wants to have 12 participants in each cell.
3. Calculating the total number of participants:
- There are 6 cells.
- If each cell has 12 participants, then the total number of participants required is:
[tex]\[
6 \text{ cells} \times 12 \text{ participants per cell} = 72 \text{ participants}
\][/tex]
So Dr. Stephens needs to recruit 72 participants.
Therefore, the correct answer is: 72.
