Final answer:
A clinical psychologist studies the impact of hospital treatment on children's brains, a developmental psychologist compares their growth to that of normal children, a cognitive psychologist examines problem-solving performance, and a counseling psychologist focuses on the children's emotional response to the hospital setting.
Step-by-step explanation:
In studying hospitalized children, a clinical psychologist might look at how their brains were affected by the hospital treatment, assessing potential psychological disorders and the impact of the treatment on mental health. A developmental psychologist would compare their growth to normal children's growth, studying aspects of physical, cognitive, and psychosocial development, while a cognitive psychologist might study the children's performance at problem-solving, focusing on cognitions, thoughts, and their relationship to experiences and actions. Lastly, a counseling psychologist would focus on how the hospital setting affected the children emotionally, aiming to improve their emotional and social wellbeing.