True or False: A synthetic worker lives on a Datadog-managed host after spinning up a private location.

A synthetic worker is an instance used in Datadog synthetics to run browser and API tests. When a private location is set up by users, the synthetic workers are not deployed on Datadog-managed hosts but rather on users' infrastructure within the private location specified. This allows for controlled testing environments and helps in keeping the test data and environments closely aligned with the user's network or system setup.

Since synthetic workers operate on user-managed resources when using a private location, the statement is false. This distinction is critical for understanding how Datadog allows users to configure their monitoring and testing environments while also ensuring that sensitive operations can be conducted securely within a user's own infrastructure.