SNES QUESTION

Does this sound right. I sold this game on the Bay and the person is sending it back for the following reason. I did not know you could save worlds. Can You? Thanks

Super Mario World (Super Nintendo)

Hi,
I ordered this item from you. I noticed when I started playing it that my nintendo will not save the information from the game. Every time I beat a world, and turn the power off it starts completely over and does not save any data. I appreciate your customer service you contacted me regularly during the sell, and I appreciate the fast shipping, but I have to return this item. If you happen to have another copy of the same item. I would love to just have another copy. If not I need a refund. Thank you

I remember the SNES had the ability to save games. Mario World had this option. I think it might have been some sort of RAM that held the game info. Maybe it's shot.