Jquery Checkbox control not working as expected

Question

If the selected option is not nil, the checkbox is checked. When the option is nil, it is not unchecked.

$('#gradable_items_wrapper select').change ->
  selected_option = $("option:selected", @)
  gi_id = selected_option.data('gradable_item_id')
  the_checkbox = $("#flightlesson_gradable_item_ids_#{gi_id}")

  if selected_option.val() == ''
    the_checkbox.prop('checked', false)
  else
    the_checkbox.prop('checked', true)

If I make one of the options "Test", and do the following...the checkbox is unchecked. For some reason '' is not being evaluated correctly above.

$('#gradable_items_wrapper select').change ->
  selected_option = $("option:selected", @)
  gi_id = selected_option.data('gradable_item_id')
  the_checkbox = $("#flightlesson_gradable_item_ids_#{gi_id}")

  if selected_option.val() == 'Test'
    the_checkbox.prop('checked', false)
  else
    the_checkbox.prop('checked', true)

I need to check a box if any option is selected in the select and unchecked if the blank option is selected.

  <div class="well" id="gradable_items_wrapper">
    <select id="gradable_category_gradable_item_<%= g.id %>">
  <option value=""></option>
  <option value="Intro" data-gradable_item_id="<%= g.id %>">Intro</option>
  <option value="Discussion" data-gradable_item_id="<%= g.id %>">Discussion</option>
  <option value="Review" data-gradable_item_id="<%= g.id %>">Review</option>
</select>
  </div>