There was a question on this quiz asking about whether bias is accounted for by the margin of error.  Students don’t really grasp how bias and error are different.  Bias is due to issues with the data collection while error is due to expected sampling variation.  Part of this is due to how students use the word “error” in everyday language.  We think of error as a bad thing.  In a survey, error is expected because we know that all samples vary from the population.  Error is ok, bias is not.

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To hammer down the point that the margin of error does not account for bias, when I give back the quizzes the next day I tell the students I have something really serious to discuss.  “If you cheated on the quiz, I need you to raise your hand.” I tell them.  Probably only one student raises their hand (I tell the first person who comes to class that day that I need them to raise their hand when I tell them to.)  Students are sufficiently terrified by this point.  “Ok, one person out of 32.  So let’s make that a 95% confidence interval for the proportion of students who cheated on the quiz.”  Then I go through and make the confidence interval, still very serious, and we find the interval is (-0.029, 0.092).  “So, I can expect that between 0% to 9.2% cheated on the quiz.  Do you think that’s accurate?”  Students hopefully at this point realize this is a ruse and relax a little and say it is not accurate because no one is going to admit that they cheated in front of the whole class to the teacher.  We talk about how margin of error is only as good as the data it comes from.  If the data is inaccurate, the confidence interval is inaccurate also.

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***You could quiz after lesson 7.4 instead of after lesson 7.3.***