Questions: A scientist is conducting a study on the effect of eating chocolate and overall mood. They believe that gender is a significant factor. The participants are divided by gender. Then, within each group, participants are randomly assigned to consume either chocolate or a placebo and then rate their mood for the day. This experiment will run for two weeks. Which type of experimental design does this situation describe? Matched-Pair Design Randomized Block Design Completely Randomized Design Case-Control Design

Solution Steps

This situation describes a Randomized Block Design because participants are first divided into blocks based on gender, and then within each block, they are randomly assigned to either consume chocolate or a placebo.

The participants are divided into two gender groups: males and females. The male participants are \( M = \{M1, M2, M3, M4\} \) and the female participants are \( F = \{F1, F2, F3, F4\} \).

Each participant within their respective gender group is randomly assigned to either consume chocolate or a placebo. The assignments are as follows:

• Males:

  • \( M1 \rightarrow \text{chocolate} \)
  • \( M2 \rightarrow \text{chocolate} \)
  • \( M3 \rightarrow \text{placebo} \)
  • \( M4 \rightarrow \text{chocolate} \)

• Females:

  • \( F1 \rightarrow \text{chocolate} \)
  • \( F2 \rightarrow \text{placebo} \)
  • \( F3 \rightarrow \text{placebo} \)
  • \( F4 \rightarrow \text{chocolate} \)

The final assignments can be summarized as:

• Males: \( \{M1: \text{chocolate}, M2: \text{chocolate}, M3: \text{placebo}, M4: \text{chocolate}\} \)
• Females: \( \{F1: \text{chocolate}, F2: \text{placebo}, F3: \text{placebo}, F4: \text{chocolate}\} \)

Final Answer