Page Example isn't using its custom page-example.tpl.php

I created a new page at mydrupalsite.com/example by following these steps:

enabled path module
added a Page using node/add/page
and set its URL path settings to "example"

I want to theme this page differently, so I defined page-example.tpl.php for it

but I still see it using the default theme not its custom tpl.php. I cleared the cache and it's still the same. Is there anything I could be missing?