Final answer:
The most important task is to give Mrs. Carpenter the call light for the purpose of ensuring her safety by providing a means to call for assistance if needed.
Step-by-step explanation:
When leaving Mrs. Carpenter alone in her room, the most important task for the nursing assistant is to give her the call light. This ensures that Mrs. Carpenter can quickly and easily call for assistance if she needs it, which is crucial for her safety and well-being. It is essential for patients to be able to communicate with healthcare staff, especially when they are alone, to address any immediate needs or emergencies that may arise.