Use an
nth-of-type selector.
:3 is nonsense.
$("#interview-accordion h3:nth-of-type(3)").addClass( "ui-state-disabled" );
It's a CSS3 selector. You can use it in jQuery selectors, native API selection, and CSS style sheets.
If for some reason you can't use CSS3 (you're working on something for the US Navy, using Windows XP, doh!) jQuery has the :eq() extension. It is ONLY usable in jQuery selectors - not as CSS selection in a style sheet, etc.
$("#interview-accordion h3:eq(3)").addClass( "ui-state-disabled" );
:eq(3) is easier to write. I don't know which one is more performant. :eq() has the simplicity of simply selecting one element from a list of selected elements. nth-of-type() has the advantage of only selecting a single element in the first place. And performance is not likely an issue here.
Just be aware of the limitations of jQuery selector extensions - they can only be used as jQuery selectors as they are not real pseudo-selectors.