Final answer:
The child in the scenario would fit best into Piaget's preoperational thought stage, as they demonstrate a limited understanding of cause-and-effect relationships.
Step-by-step explanation:
The child in the scenario would fit best into Piaget's preoperational thought stage. This stage typically occurs between the ages of 2 and 7 years old. During this stage, children can use symbols to represent words, images, and ideas. They may engage in pretend play and begin to use language. However, they do not yet understand adult logic or the concept of conservation, which is the idea that quantity remains the same even if appearance changes. In the scenario, the child's belief that the doorbell rang because the dog barked demonstrates a limited understanding of cause-and-effect relationships.