Checkboxes: how do I set the default values or show the user defined values using Form API?
From Drupal.org:

$form['element_id'] = array(
  '#type' =&gt; 'checkboxes',
  '#options' =&gt; array(1 =&gt; "One", 2 =&gt; "Two", 3 =&gt; "Three"),
  '#default_value' =&gt; array(1, 3),
);


Default value is set as an array representing keys of selected options.

Looking at the code in your question, problem is with spelling. you are setting '#deafult_value' when you want to set '#default_value'.