Change background by radio selection

HTML

<form name="form" id="form" onsubmit="return check()">
    <p><input type="radio" name="bg" value="no" /> Desactivate</p>
    <p><input type="radio" name="bg" checked="checked" value="yes" /> Activate</p>
    <input type="submit" />
</form>

JavaScript

function check() {
    if ($("#form input[name=bg]:checked").val() == "yes") {
        $('body').css('background', "red");
    } else {
        $('body').css('background', "");
    }
    return false;
}