On formal nights on Princess( we have been on the Grand and Golden) everyone( male) we saw had on at least a tie. The proportion of tuxes is not high, may be 15 % , but most men had on suits, and a few had no jackets but wore ties and dress slacks.
Almost every female was dressed up, some in ball gowns and sequins, or at least in a nice dress/ fancy pant suit and heels.
We never saw any " slobs" ( shorts, flip flops etc) , but of course the term " formal wear" is open to interpatation. Dress up like you would for a nice dinner in a fancy restaurant, or a wedding, and you will be fine.