еще вариант
<body>
<select class="spisok">
<option value="0" class="no_select" disabled selected>Выберите ваш район</option>
<option value="1">Район1</option>
<option value="2">Район2</option>
</select>
<input type="radio" name="delivery" value="1" class="delivery-item" id="del-type-1">
<input type="radio" name="delivery" value="2" class="delivery-item" id="del-type-2">
</body>
<script type='text/javascript' src='http://code.jquery.com/jquery-1.9.1.js'></script>
<script>
(function ($) {
$(function () {
$('select.spisok').change(function () {
$('#del-type-' + this.value).prop('checked', true);
});
$('input[name="delivery"]').change(function () {
$('select.spisok').find('option[value="' + this.value + '"]').prop('selected', true);
});
});
}(jQuery));
</script>