America's future
The prof in the class I'm TAing gave a pop quiz today in lecture. I graded 108 quizzes, about half of the stack. The class size is a little under 300, so this means that slightly over 2/3 of the class showed up to lecture (and felt that it was worth handing their quiz in to us
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What I originally did was
rate of cheating = (number who had copied correct answers)/(number who answered correctly + number who had copied correct answers) = 4/44 = ~9%
But I'm also thinking that
rate of identifiable cheaters = rate of cheating * rate of answering correctly
4/108 = rate of cheating * 40/108
rate of cheating = 10%
Both assume that cheaters are completely ignorant as to whether the person whose paper they're copying is answering correctly or not.
Which formula is better I think has to do with whether or not we're drawing with replacement. And I'm also too tired to think more about that.
This is already like 10X harder than the math problem that they had to solve today.
Edit: Oh, the second equation is wrong because cheating and answering correctly are mutually exclusive events. They could only be multiplied if they were independent events.
Hmm.
x = # who cheated
y = # who answered incorrectly but honestly
40 = # who answered correctly
4 = # who copied off of those who answered correctly
108 = total test-takers
x + y + 40 = 108
4 = x * 40(40+y)
...
This comes out the same as the first equation. x = 108/11, so rate of cheating = 1/11.
It also assumes that cheaters are rare enough that they don't end up cheating off of each other.
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