How to display a category in a page?

I want to display a Category in a “Page” because I have a Contests page and want to just display all the Contest entries in it. I created a Contest Page and put what I thought was the right code in there:

<?php query_posts('cat=15&showposts=10'); ?>

<ul>
  <?php while (have_posts()) : the_post(); ?>
  <li><a href="<?php the_permalink() ?>"><?php the_title(); ?></a></li>
  <?php endwhile;?>
</ul>

But it’s not displaying anything. Am I right to create a new Page to display a category for a “Contest” page?

thanks,
shane