JQuery :: Getting Radio Button Changes Some Paragraph Text

I have code that initially sets a radio button and then changes some paragraph text based on the value of the radio button. After this initial setting, I want the user to be able to change the radio buttons and get changes to the paragraph text. Currently, the code allows a change to the radio button and it shows on the screen, but the value does not change so the paragraph text does not change. I tracked this down by looking at alerts. How do I get the click on the radio button to register a change in the radio button value in jQuery? Here's the simplified code.

$(function() {
//Initialize country
$('input[name="country"]:first').attr('checked', 'checked'); //Set first radio button (United States)
alert('|' + $('input[name="country"]').attr("selected", true).val() + '|1st');
//Enable changes to the country selection and change page text as the selections change
$('input[name="country"]').change(function ()
// change the page per this logic
switch ($('input[name="country"]').attr("selected",true).val()) {
case 'United_States':
alert('|' + $('input[name="country"]').attr("selected", true).val() + '|3rd');
$('#stateMessage').text('Select a state or territory of the United States.'); break;
case 'Canada':
alert('|' + $('input[name="country"]').attr("selected", true).val() + '|4th');
$('#stateMessage').text('Select a province or territory of Canada.'); break;
default:
$('#stateMessage').text('Test - all other');
};
}).change(); // not clear what this change() does. Its in a jQuery example, but code works w or w/o it.
// Autocomplete jQuery code here which works
});
<p><label for="country">1. Click a country: </label>
<input type="radio" id="unitedStates" name="country" value="United_States">United States
<input type="radio" id="canada" name="country" value="Canada">Canada</p
<p id="stateMessage"> 2. This text should change as radio buttons change.</p>