What is the best resolution for creation of graphics for FCPX?

Hi-  What is the best resolution for creation ofgraphics for FCPX?  I had a graphics person
create me a 1920 x 1080 graphic template in Photoshop for our hospital but it
was only 76 kb and looked fuzzy on a large monitor.  What instruction should I give to get a
larger file size and higher resolution when creating graphics for a 1920x 1080
fcpx video ?

I'm sure someone with more specific graphics experience will chime in, but I would personally not create anything less than 3840x2160 as it's the same aspect ratio as your 1080 deliverable, but you can also scale it or give it movement if you want. Or if you later decide you need to deliver at a higher resolution, you're already set for that. Just my 2 cents.

You should look at this MacBreakStudio 376 from Steeve and Mark... it does miracle for graphics

You size was fine, should have been also set to 72dpi in PS. Did you actually verify the frame size of the graphic? My bet is it was much smaller than 1920x1080. Open it in Preview, Cmd-i to open the Info window, look at the Image Size and DPI. I bet you find a problem there.

Thanks to all.  Doug- you're suggestion makes sense and if I have to have the graphics department redo I will have them create it large. 
Francois -  the MacBbreak info is great and clearly the professional way
to go but would test my skill level and will go there if I have to. 
Ben, and all  - - interesting- when I open the file I received from the
graphics department Finder says size is 75 kb.  When I then open it in
PS it says it's 5.9mb at 72 pixels/inch and 1920 x 1280.  That totally
confounds me.  I'm sure it's something I'm ignorant of but how can that
be?