Problems with jQuery

I am fairly new to jQuery and I am having trouble to have it work consistently. Here is the simple example that’s not working:

HTML:

<p>If you click on the "Hide" button, I will disappear.</p>
<button id="hide">Hide</button>

My JS script:

jQuery(document).ready(function($){
  $("#hide").click(function(){
    $("p").hide();
  });
});

I checked in the source that both the jQuery script and my own script are referenced (the 2 jQuery lines by default and my script by using wp_enqueue_script()):

<script type='text/javascript' src='http://www.mine2learn.com/wp-includes/js/jquery/jquery.js?ver=1.10.2'></script>
<script type='text/javascript' src='http://www.mine2learn.com/wp-includes/js/jquery/jquery-migrate.min.js?ver=1.2.1'></script>
<script type='text/javascript' src='http://www.mine2learn.com/wp-content/themes/twentythirteen/js/test_alt.js?ver=3.7.1'></script>

If I click the hide button, nothing happens. “Normal” JS functions in the same script work, so I know that the reference to this script is working, but not any jQuery.

At some point in the past, I already had jQuery working, but I don’t know what’s different know. Can anyone help and point me in a direction where to dig? I’m out of ideas.

Thank you.