Take a look at Configuring custom storage for media libraries. I guess if you enter
F:\MediaTest to Settings -> Content -> Media -> Media libraries folder you can move the whole media library to different drive.
When you change the location of the media library folders, the system does NOT automatically move existing media files and sub-folders to the new location. To ensure that your media content is accessible and works correctly, you need to manually move the files from the old location to the new one in the file system. You have to copy your media library to
F:\MediaTest\<site code name>\...
P.S. You can't just move out one folder from media library - you have to move the whole media library.