My problem was that the active camera didn’t change after pressing <ctrl> + <num0> or using the view-menu. It switched to the new camera and selected it but the renderer rendered to the old camera.
I saw in the Outliner that the camera-icon does not change the highlight.
My problem was solved by clicking on the icon in the 3d-view-menubar which I marked on the second foto. After that I could normally change the active camera with the shortcut shown in the tutorial. 
