Which would be correct The Smiths with an apostrophy or without when printing invitation and noting who the hosts are?

The correct way to write it on an invitation is "The Smiths" without an apostrophe.

Here's why:

* Apostrophes indicate possession: "The Smiths'" would mean something belongs to the Smiths, like "The Smiths' house."

* For a plural group: When referring to the family as a whole, you use the plural form without an apostrophe: "The Smiths are hosting a party."

So, your invitation should read: "Hosted by The Smiths"