Can't comment specifically on the Jewel, but on the Spirit, they were pretty lax about it, even in the "nicer" MDR. It seemed to depend on how crowded it was. Very early at dinner when people were still just trickling in, I saw grown men in shorts allowed to enter, yet when there was a wait at the more "casual" MDR, they turned people in shorts away (I think kids under 13 are ok with shorts, but don't quote me on that).

Overall though, the Freestyle mentality is VERY lax. I am only 24 (was 22 on the cruise in question) and actually wore a tux on formal night (nothing super fancy, just a simple black ensemble, which actually cost me less than some of my suits) and I was one of maybe 10 men on the ship in anything fancier than a sport jacket. An older gentleman actually came up to me the next morning on deck and said he was amazed people my age actually had class and knew how to dress on a ship.
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Past Cruises:
1/2015: Adventure of the Seas - Eastern & Southern Caribbean
5/2009: Norwegian Spirit - Bermuda
8/2005: Voyager of The Seas - Western Caribbean
8/2003: Serenade of The Seas - Canada & New England Inaugural Public Voyage
6/2003: Majesty of The Seas - Bahamas