Originally Posted by HomelessScientist

This is not correct--the atmospheric pressure outside the ball decreases at higher altitudes, while the pressure inside the ball stays the same, so the pressure differential (which is what matters for the basketball's structural integrity) goes up.

Having said that, let's look at the numbers. A basketball is typically inflated to a "gauge pressure" (pressure differential with respect to the prevailing atmospheric conditions) of about 7 to 9 psi (pounds per square inch; apologies to those of you who use sensible units). At sea level, the absolute atmospheric pressure is about 15 psi; it goes down to 10.5 psi at 9000 feet, which would be a typical cabin altitude. That means the gauge pressure of the basketball would go up by 4.5 psi, or about 50%. I don't know what kind of safety factor they build into basketballs, but you might be pushing it. I would let some air out of the ball if I were you.