Please Help me with this

Based upon Chapter 8 of (Legal and Ethical Essentials of Health Service Administration)

Please read this scenario on the legal doctrine Respondeat Superior.

"A patient comes to an emergency room complaining of hip pain. The ER physician conducts an examination and orders X-rays as part of that exam. The attending radiologist is a physician who works for Acme X-ray. Acme X-ray is a contractor that provides radiology services to hospital emergency rooms. The hospital pays Acme and Acme pays the MDs. The hospital gives all control to Acme related to Radiology in the emergency room. An Acme radiologist reviews the films and misses a hairline hip fracture. The ER physician based upon the radiologist report discharges the patients with Advil for pain. One week later the patient goes to another ER and the hairline fracture is picked up. The patient has hip surgery."

Question: While in recovery, the patient hires an attorney who sues the radiologist and the hospital. Is the hospital liable? Explain your answer using legal principles.