Final answer:
The task of determining the time of death for the family should not be performed by a CNA in hospice care; this is a responsibility for licensed professionals such as nurses or physicians.
Step-by-step explanation:
The task that should not be performed by a Certified Nursing Assistant (CNA) in hospice care is determining the time of death for the family. This responsibility falls within the scope of practice for licensed professionals such as nurses or physicians, who receive special training for end-of-life care and are legally authorized to make this determination. CNAs play a critical role in providing comfort and support by performing tasks like taking vital signs, providing repositioning and perineal care for the patient, and offering emotional support for the family. However, they do not have the qualifications or legal authority to officially declare the time of death.