This statement is true.
Burrhus Frederic Skinner was an American psychologist and social philosopher. He considered the free will an illusion and believed the human action is the consequence of previous actions.
Skinner believed that children learn a language through operant conditioning, meaning they receive a reward for using language in a functional manner. His formula for learning language is based on four terms: motivating operations, discriminative stimuli, response and reinforcing stimuli. He suggested that children learn language through imitation of others through prompting ans stimulation.
Toddlers with small vocabularies were exposed to poor verbal communication with their parents. If the parents had talked to them more, they would have felt stimulated to respond to them and would learn new words and develop their vocabulary. Being around non-talking parents deprived them of the need to talk because they did not see any rewards in learning the language. They did not feel stimulated enough to talk and that is why their vocabulary is small.