The Obama administration is investigating pay practices throughout the health care industry after finding that many hospitals and nursing homes do not pay proper overtime to nurses and other employees who work more than 40 hours a week. Hospitals around the country have paid millions of dollars in back wages to settle claims by the government and their employees. And many more hospitals are fighting class-action lawsuits that raise the same issues. In St. Louis, the Labor Department has recovered more than $1.7 million in back wages for 4,000 employees of hospitals and clinics operated by SSM Health Care, a Roman Catholic system. In Boston, the Partners HealthCare System agreed to pay 700 employees more than $2.7 million in overtime back wages to resolve a lawsuit by the department alleging violations of the Fair Labor Standards Act. And under the proposed settlement of a class-action lawsuit in California, Kaiser Permanente would pay $7.25 million to hundreds of registered nurse coordinators, case managers and other medical workers. The employees said they had been denied overtime pay because they were improperly classified as exempt. Kaiser denied wrongdoing but has agreed to the settlement.