My 1st tube amp: transformer buzz audible 15 feet?

If this is a new unit and the shop is local tell them you want a replacement. You should not hear any buzz coming from the transformer. Do try a cheater plug which will lift the ground
Also you could bring the unit to the dealer, hook it up and see if it buzzes. If it does demand a new unit
Alan

Jaybo is correct times 3.
You don't have to suffer in this hobby.
In fact it should be outlawed.
Nervosa maybe nothing worse.

It could be that you have DC on the line. I had this problem in my last apartment with my FirstWatt F1. There are two devices you can get to solve the problem (if it is in fact DC on the line!): the PS Audio Humbuster and the CI Audio XDC-2. Both are sold with 30 day money back guarantees, so if they don't fix the problem you are only out shipping costs. Both companies often have these as B stock as well.

May be that this isn't your problem, but solved my chassis hum problem pronto. One way to tell if DC might be the problem: was there an hum when plugged in at the audio shop you bought it from?

It is not necessarily the amp that is defective.

Does it make this hum regardless of where it is plugged in or what it is plugged into?

In my case, it was my apartment's cruddy power. The amp was a Nelson Pass designed and built FirstWatt F1. One of the best amps I have ever owned and lived with (the entire FirstWatt line is fabulous). The crappy receiver I had before the F1 didn't make this noise. Did I want the receiver back in my system? Heck no. I found the cause of the problem and fixed it. Thank you Humbuster and long live the F1.

I suggest systematically explore the issue until you determine exactly what the culprit is.

Regardless, I wish you a hum free existence.