Without looking at any raw data I'm fairly confident that the Kobe's FG% without sweatbands/sleeves is NOT within one standard deviation of his FG% while wearing some sort of arm apparel (I'm guessing the standard deviation of FG% among NBA players is somewhere around 1%, and maybe even smaller if we accounted for position).

That said, I'm also pretty sure that it's not the lack of sweatbands that are CAUSING him to shoot a lot worse, but most likely it's your classic triangular non-relationship. For example, Kobe might have stopped wearing sweatbands/sleeves more frequently later in his career when his overall shooting %s were lower, thereby creating this scenario where his stats without arm apparel are significantly worse than his stats with. Age being the 3rd variable composing the triangle here. (Not saying this is true, just giving a hypothetical example of a plausible triangular non-relationship.) In any case, the results might have some statistical significance (depending on how we want to define it), but that wouldn't necessarily mean the sleeves are the cause of the significance - this is of course the oft-repeated Statistics 101 adage about correlation ≠ causation.

Also, it's possible (but not likely) that the results here are not merely a statistical accident relating to triangular non-relationships or randomness or sample size etc but rather a legitimate, actual discovery that wearing something on his arms helps Kobe shoot better. I strongly suspect that's not the case but it's just plausible enough that I can't dismiss it outright without seeing some more research. (Which of course I won't do because I'm fat and lazy and eat too much fast food. It's a lot easier to write a few paragraphs about statistical research than actually doing any of it yourself. Let the peasants do the grunt-work I say!)