Which Amazon service provides a managed environment for running Apache Hadoop?

Amazon EMR, or Elastic MapReduce, is the correct choice because it is specifically designed to provide a managed environment for running big data frameworks, including Apache Hadoop. EMR simplifies the process of setting up, configuring, and tuning big data frameworks, allowing users to quickly and efficiently process vast amounts of data without needing to manage the underlying infrastructure.

EMR automates tasks such as provisioning resources, inspecting data, adjusting configurations, and managing scaling, which can significantly reduce the complexity and time needed to run Hadoop jobs. This service integrates seamlessly with various AWS data storage solutions, making it a powerful tool for data engineering, analytics, and machine learning workloads.

In contrast, while Amazon ECS (Elastic Container Service) focuses on container orchestration, mainly for running Docker containers, and Amazon EC2 (Elastic Compute Cloud) provides scalable virtual servers, they do not offer the specialized support for running Hadoop. Amazon RDS (Relational Database Service) is designed for relational database management and does not support the Hadoop ecosystem. Therefore, for tasks specifically involving Apache Hadoop, Amazon EMR is the most suitable and effective service.