How does cholesterol affect the fluidity of a plasma membrane?
Cholesterol certainly affects plasma membrane fluidity. In 1978 Cooper found that increasing the ratio of cholesterol to phospholipids decreased the membrane fluidity. This also reduces membrane permeability and reduces the survival of the cells (red blood cells in that case). I imagine this is where the textbooks draw their conclusions.

More recently Rog et al., 2008 demonstrated the importance of the hydroxyl group in the cholesterol by replacing it with a ketone. This affected fluidity and flip flop rate.