[jQuery] :eq() expects number problem

[mjpg]

I'm selecting an item based on using an index.
:eq(3) works but if I pass a variable it does not.

CODE SNIPPET:

function populateSelect(choosenValue) {
     // Get the optgroup options
     var choosenOptions = $('#courses optgroup:eq(choosenValue)
option');
     ....

THE FOLLOWING WORKS:

$('#courses optgroup:eq(3) option');

DO NOT SEEM TO WORK:

$('#courses optgroup:eq("+choosenValue+") option');     // and I don't
understand this anyhow

or
choosenValue = parseInt(choosenValue);
$('#courses optgroup:eq(choosenValue) option');

or
choosenValue = Number(choosenValue);
$('#courses optgroup:eq(choosenValue) option');


I'd appreciate a pointer here. I can see :eq expects a number and I'm
struggling to deleiver it.

Thanks