As someone who has had lots of economics/probability training, this quiz really doesn't do the research justice. It gets a point across, but could have been presented better. I was bothered by its misuse of terminology and the quiz not really being one.
Spoilers ahead!
1. The answer could be A or C, depending on how small and large the hospitals are. The small hospital could easily be expected to have < 5% more variance (depending on definition of "small" and what 5% of each other means) depending on its and the large one's size.
2. I don't see why the correct response must be 30%. Such attributes conditionally describe an engineer better than a lawyer. Assuming random sampling of lawyers and engineers, I'd be surprised if the answer isn't > 30%. I'm not sure what the numbers are actually, as I don't know how strong this conditional applies to engineers or lawyers.
The point of the research is that people over-emphasize the conditional over the prior (indeed often ignore the prior), not that people should not use conditional information.
3. " it is likely that your answer to question (a) is positively correlated to your answer to question (b)"
I understand what they are trying to say, but the wording is quite off. Correlation is a property of data, not an individual point. If I'm the only person who ever takes this test, my answers have undefined correlation. The modifier "likely" is especially baffling (correlation is a constant property of data).
Proper (and less verbose!) terminology is "people's answers to (a) are positively correlated to (b)"
Spoilers ahead!
1. The answer could be A or C, depending on how small and large the hospitals are. The small hospital could easily be expected to have < 5% more variance (depending on definition of "small" and what 5% of each other means) depending on its and the large one's size.
2. I don't see why the correct response must be 30%. Such attributes conditionally describe an engineer better than a lawyer. Assuming random sampling of lawyers and engineers, I'd be surprised if the answer isn't > 30%. I'm not sure what the numbers are actually, as I don't know how strong this conditional applies to engineers or lawyers.
The point of the research is that people over-emphasize the conditional over the prior (indeed often ignore the prior), not that people should not use conditional information.
3. " it is likely that your answer to question (a) is positively correlated to your answer to question (b)"
I understand what they are trying to say, but the wording is quite off. Correlation is a property of data, not an individual point. If I'm the only person who ever takes this test, my answers have undefined correlation. The modifier "likely" is especially baffling (correlation is a constant property of data).
Proper (and less verbose!) terminology is "people's answers to (a) are positively correlated to (b)"