Is it possible to assign test to specific user groups?

Yes, it is possible to assign test to specific user groups. When creating a testing session, you should choose the desired user group to whom the test will be available. Upon selecting the group, you will have to hand-pick the group members who will have access to the session or turn on the option of Self-enrollment to grant access to the whole group.

For more detailed information, please check this article, or watch this video.