I know at least one source for the misconception that carrots make your eyesight better: a WW2 lie to hide the fact of the existence of either radar or encryption breaking (I forget which).
But someone who actually believed carrots make your eyesight better might try to test it for themselves. They may even keep on deluding themselves after doing an experiment (hey, the placebo effect is strong).
What about someone who believes a juju amulet makes them impervious to stabbing. Would they be willing to try it? You offer to stab at their heart with all your might, and if they survive you give them money. Do they accept your offer? If they don't -- and they never do -- what is happening is that they suspect it doesn't really work.
It reminds me of Jack London's story, "Lost Face": https://americanliterature.com/author/jack-london/short-stor...