I recently remodeled one of our bathrooms and my wife found a great deal online for oil rubbed bronze faucet. After a few weeks I walked by the bathroom and heard the water running. I went in and noticed it was turned off. I turned it full on and backed to off and it shut off. I thought it was just an anomaly. Four days later it happened again with the same corrective action. Roughly a week later it was running in the off position but this time I couldn't shut it off. I chalked it up to poor quality of the faucet. I replaced it three weeks ago and this morning the new faucet it doing the same thing. I can't figure this out. Please help.

Very Respectfully--Jay

Remove toilet tank lid and see if water is running in tank.

No the toilet isn't running

I am assuming from your post, that you hear water running in the pipes and not that the faucet is actually leaking.
If you hear water running that means it is coming out some where. About the only place for water to come out and you not see it is a toilet or a lawn irrigation system. Opening and closing the faucet may have momentarily reduced the pressure to the toilet fill valve and allowed it to turn off.

It can be difficult to locate the source of a problem from sound alone. Sound travels extensively in pipes.

Do you have any other toilets? Do you have a lawn irrigation system. Is the sound continuous.