Test doesn't show up
Your test class look OK.

There is no need to install or enable the Simple test module if you're using Drupal 7.  Instead, you should enable the core Testing module.  (Don't know if installing Simple test will make a difference, but it were not present when I went through the routine described below.)

Provided it exists inside your module's directory, you're using Drupal 7, have enabled the core Testing module, cleared the cache, and made sure to declare your test file with the correct name in your module's .info-file, nothing should stop it from appearing in the list included in the "Examples" group when you visit /admin/config/development/testing.

Here is how it looks on my site (after I've gone through the steps outlined above):