I just want to say how much I hate it when researchers use bar charts with a higher than zero baseline in order to over-represent their findings.
It seems difficult to me to distinguish between two explanations for their findings. (1) People who give the wrong answer to the bat-and-ball problem aren't altogether unaware that they're substituting an easier problem, after all. (2) They are altogether unaware, but explicitly asking them how sure they are about their answer triggers more reflection and then they are on some level, to some degree, aware that they've fudged it.
(Maybe there is no fact of the matter as to which of those is going on. But it seems like they ought to have different consequences, even if it's really hard to disentangle them experimentally.)
Total = $1.10 Bat is 1$ more than ball.
I wonder if the visual parsing or rounding. Have someone run some obvious permutations?
1.10,1.10 +-.02 is $1,$1+-.02 more.
2.10,2.10 +-.02 is $1,$1+-.02 more.
is $2,$2+-.02 more.
3.10,2.10 +-.02 is $1,$1+-.02 more.
is $2,$2+-.02 more.
is $3,$3+-.02 more.
From the article:
Using an adaptation of the standard 'bat-and-ball' problem, the researchers explored this phenomenon. The typical 'bat-and-ball' problem is as follows: a bat and ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost? The intuitive answer that immediately springs to mind is 10 cents. However, the correct response is 5 cents.
The authors developed a control version of this problem, without the relative statement that triggers the substitution of a hard question for an easier one: A magazine and a banana together cost $2.90. The magazine costs $2. How much does the banana cost?
A total of 248 French university students were asked to solve each version of the problem. Once they had written down their answers, they were asked to indicate how confident they were that their answer was correct.
Only 21 percent of the participants managed to solve the standard problem (bat/ball) correctly. In contrast, the control version (magazine/banana) was solved correctly by 98 percent of the participants. In addition, those who gave the wrong answer to the standard problem were much less confident of their answer to the standard problem than they were of their answer to the control version. In other words, they were not completely oblivious to the questionable nature of their wrong answer.
Article in Science Daily: http://www.sciencedaily.com/releases/2013/02/130219102202.htm
Original abstract (the rest is paywalled): http://link.springer.com/article/10.3758/s13423-013-0384-5