Did fifteen out of twenty-two students somehow manage to reel off the same six consecutive correct answers (the d-a-d-b-c-b string) all by themselves? There are at least four reasons this is unlikely. One: those questions, coming near the end of the test, were harder than the earlier questions. Two: these were mainly subpar students to begin with, few of whom got six consecutive right answers elsewhere on the test, making it all the more unlikely they would get right the same six hard questions. Three: up to this point in the test, the fifteen students’ answers were virtually uncorrelated.
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