How do I check if a radio button is checked using javascript?

I am not very good at javascript but have messing around with it for a class project.

Here is my code right now:

HTML:

<form id="Resume_Select">
<input type="radio" name="resume_type" value="Economics" >Economics
<br />
<input type="radio" name="resume_type" value="MIS" >Management Information Systems
<br />
<button onClick="resume_select()"> Download</button>

</form>

Javascript:

<script>
function resume_select(){
var radios = document.getElementByName('resume_type');
for(var i = 0, length = radios.length; i<length;i++){

if(radios[i].checked){

 var resume = radios[i].value;
    alert(radios[i].value);
    break;
}


}

</script> 

When I select a radio button then click the download button, nothing happens. No alert shows up or anything.

I would greatly appreciate some input on how to improve this.

Other note, I know that it can be done easier with jQuery I have seen, but please stick to javascript. I want to learn jQuery, just not quite yet haha.

Thanks!