Final answer:
The healthcare system described is most like Medicare, which is a federal program in the United States that provides health insurance for those over 65 and certain younger individuals with disabilities, with services provided by private entities.
Step-by-step explanation:
A healthcare system which includes federal government financing and federal administration of health insurance but provision of health services by private healthcare providers is most like Medicare. Medicare is the U.S. federal program that provides health insurance to people over the age of 65 and to certain younger people with disabilities. In this system, the government funds and administers the insurance, but the actual healthcare services are provided by private entities. This is akin to the model described in the question where the federal government manages the insurance aspect, while private healthcare providers deliver the services.