Adding Google Analytics to footer selectively

You have the ?> and ?php at wrong place, this way user logged in testing is a simple text.
Try this:

// add google analytics to footer
function add_google_analytics() {
    if ( !is_user_logged_in() ) 
    {
    ?>
        <!--Google Analytics-->
        <script type="text/javascript">
            var _gaq = _gaq || [];
            _gaq.push(['_setAccount', 'UA-XXXXXXXX-X']);
            _gaq.push(['_trackPageview']);
            _gaq.push(['_trackPageLoadTime']);
            (function() {
                var ga = document.createElement('script'); ga.type="text/javascript"; ga.async = true;
                ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
                var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
            })();
        </script>
    <?php
    }
}

add_action('wp_footer', 'add_google_analytics');