Do i need to reinstall MacOS when trading in my old Macbook air?

F-i-f-i Said:

"Do i need to reinstall MacOS when trading in my old Macbook air?: To trade-in value for my old macbook , do I NEED to reinstall MacOS prior to shipment? I have completed the other sign-out and format procedures. Just didn't do the reinstall."

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What to Do:

Its not required, but is most certainly recommended, for Security & Privacy purposes. If you are looking to rid of you older Mac, be certain to disassociate it from you current account, back it up, and then install it anew. Go Here: What to do Before you Sell, Give Away, or Trade in your Mac - Apple Support

This is what Apple recommends.

What to do before you sell, give away, or trade in your Mac

It sounds like you've done most of this. Point 7, Erase your hard drive and reinstall macOS, is probably the last thing to do.