Answer briefly and with a recent example. Back your claim with a time when a manager or supervisor complimented you on your attention to detail.
"I am a very detail oriented person. My colleagues and supervisor regularly compliment me on my keen eye. Just last week I noticed that we were missing a sample from a patient. By noticing this, I was able to save a lot of extra time from the patient and work for the lab. My supervisor was very thankful that I had been paying such close attention."