This is an oldie as I did this repair a while back. But I was just looking at my Amazon wishlist for some 2002 related stuff (more on that later, I hope) and saw that I still had the oxygen sensor for the MINI saved for future reference.
So, this is as good a time as any to do a quick run down. First, what caused me to replace the O2 sensor in the first place? The SES or Check Engine light kept coming on then going off, then it would come back, then leave…you know the routine. This is almost always an oxygen sensor if you don’t immediately notice any other issues with the car. O2 sensors can start to go bad but not immediately affect driveability. I checked the OBD2 code with a code reader I borrowed from my local BMW CCA chapter and determined that it was an O2 sensor (I forget the code it threw it has been so long since I did this.) Or you can pick up scanners pretty cheap now like this Autel AutoLink scanner.
So, after much forum searching and reading I found that this Bosch 13878 Oxygen Sensor on Amazon
Firstly, I only replaced the sensor closest to the exhaust manifold before the catalytic converter. These guys see the most heat so they usually go out first. The one further down the exhaust is still kicking at 173K+ miles. The sensor I’m talking about is the #8 on the left side of the image linked here.
I was able to get to the O2 sensor without much fuss. You may need to bend the heat shield (little aluminum plate thingy) out of the way and move the coolant overflow tank or power steering fluid reservoir out of the way (I believe those are held on with 10mm bolts.) Disconnect the sensor wire at the connector before trying to remove it. Removing it does require a special socket. I used a deep well socket with a cut out that allows you to place the socket over the wire, like this one: Oxygen Sensor Socket on Amazon
Basically once you apply a little elbow grease and remove the old sensor the new one goes in and you’re done. Snug the sensor in as tightly as you can as it will be a bit of an odd angle for you to get good torque on the wrench or ratchet. Reconnect the sensor and fire up the car. The SES code should reset itself but if it doesn’t fo out after a few start/stop cycles, you can disconnect the battery for a minute and plug it back in to reset the light. If the light comes back on, re-scan the OBD2 codes (Autozone, Pep Boys, etc. will usually do this for free) and verify you don’t have something else going on. I also like to check for any exhaust leaks that may be around the new sensor. If the sensor isn’t snug enough you may be able to feel puffs of exhaust gas near the sensor.
And that’s about it. If that little yellow light is annoying you it could be your O2 sensor!