Find a selector and update

I have a three different radio buttons and based on the selection of the radio button I would like to capture which radio button the user clicked and store that in a hidden input textbox for later use.

Here is the code I have tried, which doesn't seem to be working:

//clicked on first radioButton:

     $('#Employee').change(function () {
        if (this.checked) { 
            $('#multi').show();
            $('#Type').attr("EmployeeSelected"); 
         }
    });

//clicked on second radioButton:

    $('#Employer').change(function () {
        if (this.checked) { 
            $('#multi').show();
            $('#Type').attr("EmployerSelected"); 
         }
    });

My page looks like this:

<fieldset id="multi" class="fieldset-auto-width">
 <legend>
        Selected Form
 </legend>

<form action="/PostToDb" method="post">        
   <input type="text" name="Type" value="xx" />

  <div>
    ......................
  </div>
</form>

How do I update the textbox to whichever radio button is selected?