"If I am sure I'm right, I would ask him or her why I'm wrong. After all, I may be wrong. If his or her rationale doesn't justify the conclusion with which I disagree, I would ask for a third party to render another opinion."

This is more than just conflict resolution, but conflict resolution with a person superior to you. That adds additional drama as to whether you should champion your position which may cost favor with your superior. Life is short and you must choose your battles carefully, but the interviewer wants to hear that in disagreements which jeopardize patient care, you're willing to go down to the mat for that patient. Any of the sample answers can be modified with a specific anecdote you want to relate.

"If the disagreement were trivial, it is my place to obey my superior; if it were to have a major impact on the patient's health or safety, I would insist our disagreement go up the chain of command for a resolution in the patient's best interests."