Since I have time to spare (and am obsessed with statistical analysis…and love to flaunt my useless knowledge), here are the locations of the toilet paper rolls in some of the hotel rooms at the hotel I used to work at:
201: right
202: both
203: left
204: right
205: right
206: left
207: right
210: right *
211: left
214: right
215: left
216: left
217: right
301: right
302: left
303: right
304: right
305: right
306: left
308: right
309: left
310: left
311: right
312: right
313: left
314: right
315: right
316: left
*The bolded rooms are where the placement seems to truly be arbitrary. For instance, in room 312, the toilet is surrounded by walls on all but 1 side.
In the rooms which the toilet paper does not seem to be arbitrarily placed, the placement is consistent based on the wing. One wing is more renovated than the other, which is my hypothesis as to why the pattern suddenly changes. In one wing, rooms 201–207 (202 an exception) and 301–306, the toilet paper is placed between the toilet and the sink. In the other wing, rooms 214–217 and 308–316, the toilet paper is placed on the wall next to the toilet but not next to the sink. So, it has nothing to do with left/right preference.
However, take a look at the bolded rooms where it really did seem like a tossup. In all but one of them, the toilet paper is places on the right. This goes against your conjecture.
In fact, in the “older rooms” where the toilet paper is between the toilet and the sink, it’s pretty awkward to access it, and I think it’s in part because the holder is mounted really low. I suppose they realized that when they renovated, so this factor may skew the results.
More statistics:
The toilet paper in my bathroom here is on the right between the sink and the toilet.
The toilet paper in my parents’ house’s bathrooms are both on the right.
The toilet paper where I used to live was on the left.
The toilet paper in another place I used to live was on the right.