Final answer:
The best experimental design for the given scenario with two factors - type of breakfast and time of eating breakfast - affecting body mass index, and with participants randomly assigned to groups is a completely randomized factorial design (CRF).
Step-by-step explanation:
To determine which experimental design is most appropriate for studying the effects of type of breakfast and time of eating breakfast on body mass index, we need to analyze the setup of the experiment.
In this case, we have two factors: type of breakfast and time of eating breakfast, with the participants being randomly assigned to one of the groups formed by the combination of these two factors. Each participant is in only one group and does not experience the other groups' conditions.
Since we have a factorial design where each participant is in only one group, the best fit would be a completely randomized factorial design (CRF).