Mediawiki make it quite clear that it is not the best product if you want to create and manage private pages for specified users. However, it is possible to set up group based access to pages using the Mediawiki group access extension. This link takes you to the instructions on how to install the extension and how to use it to make pages private to groups of users. You can also download the extension files.The following text is added to the localSettings.php file:

require_once(“extensions/accesscontrolSettings.php”);
include(“extensions/accesscontrol.php”);

It may be necessary to edit the contents of the accesscontrolSettings.php as instructed. One thing that needs doing here is to uncomment the english version lines and comment or delete the german version lines. Another edit I made was to make a No_Access page display within the wiki. To do this I had to create the No_Access page and edit the following line:

$wgAccessControlNoAccessPage = “/index.php/No_Access”;
This took the reader to the WP installation 404 page and therefore outside of the wiki.

$wgAccessControlNoAccessPage = “../index.php/No_Access”;
This takes the reader to a no access page I created within the wiki.

In another installation I did a year or so ago sometimes an access controlled page would appear to be public still. I found the following fix, to disable caching, on the talk page to the above extension page:
Mediawiki group access extension: Talk page

$wgMainCacheType = CACHE_NONE;
$wgMessageCacheType = CACHE_NONE;
$wgParserCacheType = CACHE_NONE;
$wgCachePages = false;

A warning indicates that this is necessary for the access controls to work properly.