As the government continues to gather data on how satisfied patients are with their hospital stays, skeptics in the health-care community grumble that what really matters is the quality of treatment and how well people fare after going home. It turns out that satisfaction and quality are related, according to a new study from Cooper University Health Care. Previous research has found some evidence of an association between the quality of medical care and patients' opinions of it, and there are a variety of reasons that might explain why it is true. But the new study is apparently the first to find such a connection with the five-star ratings, introduced last year by the U.S. Centers for Medicare & Medicaid Services.