I know that competency interviews are set up for those with education and not too much experience and the company wants to know how you would handle certain situations that may come up.
There is actually no real wrong answer they are looking to see if the candidate is driven so to speak to resolve crisis situations, complete projects, get along with team workers, etc.
Here is an example;
"Have you ever NOT completed a job or project?"
"During my final year at university I failed to deliver my dissertation on the due date. This was because I was heavily involved in cutting edge research right up until the end of my course and was waiting for imminent results from surveys being undertaken by researchers at other academic institutions.
Considering this was my final piece of academic work, I wanted to ensure it was based on the most accurate and up to date sources of information available, even if this meant a delay in production. To ensure no marks were deducted from my dissertation, I contacted my course director and personal tutor two weeks before my dissertation due date to discuss my particular situation. I argued my case, and was consequently allowed an extra two weeks to produce my work.
Although my work was delayed, I feel that this delay was justified in that the work was of the highest quality it could be. Furthermore, I sufficiently organised myself in relation to my department and tutors, so that all relevant people were aware of a possible delay in the production of my dissertation."
A negative, turned positive....
Hope this helps in some small way red.