What is the standard for federal courts to establish jurisdiction over a case?

The correct choice is subject matter jurisdiction, which is the authority of a court to hear cases of a particular type or cases relating to a specific subject matter. In the context of federal courts, subject matter jurisdiction often involves cases that arise under federal law or involve parties from different states (diversity jurisdiction).

Federal courts have limited jurisdiction as determined by either the Constitution or federal statutes. For instance, they can hear cases that involve federal questions (those arising under the U.S. Constitution, federal laws, or treaties) or cases where the parties are of diverse citizenship, meaning they are from different states and the amount in controversy exceeds a specified threshold.

Establishing subject matter jurisdiction is essential; without it, a federal court cannot proceed with a case. Therefore, understanding the concept of subject matter jurisdiction is crucial for recognizing when a federal court can hear a particular case, making it the correct answer to the question regarding the standard by which federal courts establish their jurisdiction.