you need to specify the post_type in your $data
array :
$data = array(
'post_type' => 'classifieds',
'post_content' => stripslashes($output),
'post_title' => stripslashes($title),
'post_date' => date('Y-m-d H:i:s'),
'post_category' => array($cat_ID),
'post_status' => $statusPost,
'post_author' => $post_author
);