jQuery not adding class to body

I'm trying to add a class to the body when someone is viewing the page on a mobile device. I have got the mobile detection down, but for some reason jQuery won't add a class to the body tag. I am stumped as to why it isn't working. I get the alert with 2nd but no mobile class.

(function () {
        var NO_REDIRECT = 'noredirect'; // cookie to prevent redirect
        // I only want to effect phones
        if (isMobile.any) {
                alert('1st')
                // Only redirect if the user didn't previously choose
                // to explicitly view the full site. This is validated
                // by checking if a "noredirect" cookie exists
                if ( document.cookie.indexOf(NO_REDIRECT) === -1 ) {
                    alert('2nd');
                    $(document.body).addClass('mobile');
                }
            }
        })();