compruebe si la consulta da como resultado una fila vacía mysqli

Puede usar num_rows en el conjunto de datos para comprobar el número de filas devueltas. Ejemplo:

$results = $mysqli->query("SELECT ANNOUNCE_NUMBER,ANNOUNCEMENTS,ANNOUNCE_TYPE,POST_DATE FROM home WHERE ANNOUNCE_NUMBER NOT LIKE $excludewelcome AND ANNOUNCE_NUMBER NOT LIKE $excludenews ORDER BY ANNOUNCE_NUMBER DESC LIMIT $position, $items_per_group");
if ($results) { 

    if($results->num_rows === 0)
    {
        echo 'No results';
    }
    else
    {
        //output results from database
        while($obj = $results->fetch_object())
        {
            if($obj->ANNOUNCE_TYPE=='NEWSEVENTS')
            {
                $realstring='News and Events';
            }
            else
            {
            $realstring='Welcome Note';
            }

            echo '<li id="item_'.$obj->ANNOUNCE_NUMBER.'"><strong>'.$realstring.'</strong></span>';
            echo '<br \>'; 
            echo '('.$obj->POST_DATE.' ) <span class="page_message">'.$obj->ANNOUNCEMENTS.'</span></li>';
        }
    }
}