you might get lucky by going to HD or Lowes, Bring the whole lamp with you.
You might end up with an experienced guy who knows something and be able to fit it for you right there and test it. It is hard to say if the replacement you got now is correct without looking ....but the t-8 and T-10 should have the same connectors....This time around when mine burn out I'm switching to LED
so I can get the moonlight and daylight in the Same fixture. Right now I have Blue LED
's from QVC attached to the lamp with timer and Battery pack.