While looking at the new first page of the new sub-subsite, click in your browser's Address box and replace the file name you gave with "admin", producing a new URL like
Press the "Enter" key in order to bring that sub-subsite administration page up in your browser.
Observe the sub-subsite identification in the box near the upper right corner of the page, to confirm that your commands will affect the correct sub-subsite.
Click on the plus-sign [+] to the left of the heading "General Security" to drop down the choices.
Click on "click here to manage subsite level security."
Find the check-box with the title "Inherit Security From Parent" and if it is not clear, click in it to clear ("un-check") it. That will display the expanded list of access permissions.
Inspect the current settings, and change those that do not match your needs; for example, you might make the changes called for in the next section. You can return to this dialog later to make changes.
Click on the "OK" button.
In order to establish a sub-subsite that only the pagemasters can access (for example, to experiment), do the above, with the following particular steps at step 6:
In "General Security" click on the "pencil" icon to edit the rights for both "anonymous users" (the general public) and "authenticated users" (everyone with an OAK login ID and password), setting them both to have no rights.
In "Content Security" click on the "pencil" icon to edit the rights for both "anonymous users" and "authenticated users", setting them both to have no rights.
For both categories of user, do not click on the "X" to remove that category.