If we expect 50% of people to get the question right when they guess, we have this formula: Total percentage correct = .5n + x, where n = percentage of people who guess and x = percentage who get it right and don’t guess (The .5 being the probability of guessing right).

Plug in percent correct and n as you please and solve for x. In your example, we have 65% = .5(70) + x. x = 65% – 35% = 30%.

You can also see the equation you wrote is actually solving for the number of people who would guess if all the people who didn’t guess got it right. This is the upper bound on the number of people who guess based on the expected distribution. The lower bound is 0 and we’d have .5(0) + x = 65%. Thus x = 65% (the case where no one guessed but everyone “knew” the answer, just that 35% were wrong about what they “knew”).

What all this really means is that we have a range of 30-65% of people who actually know the answer. We have no way of telling how many people guessed, nor do we have any way of deciphering another option–that people made educated guesses while being somewhat sure of the answer based on other knowledge. In that case, we could end up with 65% getting it right but no one having been absolutely sure about it. To determine this, some more in depth questions need to be asked such as asking people to explain their answers.

]]>How about focusing on teaching evolution as a means to combat ignorance about evolution in believers and unbelievers alike? Would that be alright?

(Who refuses to teach about the physics, geology and biology involved in evidence for evolution? – oh, only the religious nutjobs? How would they feel about putting more Hume, Marx, Nietzsche and Freud into the syllabus, I wonder.)

“it’s ME vs THEM. What do you think?”

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