#27: It would be better to use the word association. In some more formal settings (AP Stat for example), correlation is reserved for linear relationships. 27 (4) would not be linear.

Agree that the wording is terrible. Also, are they talking about multiple countries or multiple census for one country? Is (2) considered non-causal because the census is a snapshot that does not capture fluctuations in the intervening years? If so, sigh…

#7: Yikes. It doesn’t make sense to say a GROUP is biased in this context. Bias would means the survey is done in a way that is likely to error on one direction. If the survey is done in a way that will tend to over-represent a group (like campers), then there is bias (assuming campers opinions differ from the population as a whole). Bias in this context does not mean “tend not to like” as in everyday language.

The wording is poor as well. Again, it doesn’t make sense to ask about the bias of a group in this case. But, what is the point of the “if” part: “If a survey were taken, which group…”. Does taking a survey affect the “bias” of the group?

#28 doesn’t bother me so much, though it would be nice to include approximately.

]]>I don’t like the question because it assumes that one can say with certainty how many students will have particular heights. The question should ask for an estimate, or a best estimate, or a confidence interval.

]]>I’m most bothered by your last normal distribution item & Jerome’s survey question. I agree, Patrick, that there is a fundamentally flawed assumption by the NY question in its claim that the finite, discrete set of high school girls’ heights were normally distributed. Jerome is also spot on with his warning about the “number of unwarranted and usually incorrect assumptions.”

Independent of the actual intended answers, the bigger problem, I think, is the assumption by both the NY and MD questions that exact, definite outcomes (“how many of the girls ARE shorter? & “how many people WILL vote “no”) can be derived from survey results and assumed normal distribution. It’s likely a small and subtle point, but no questions like these can ever give absolute, definitive predictions. The language may be standard, but statistical questions are by their nature probabilistic (duh). We should be stunned if any prognostications for any population of reasonable size were met by experimental outcomes exactly mirroring theoretical predictions.

]]>I will call your New York State statistics questions and raise it with the following assessment item on Data Analysis from the Maryland High School Assessment [MD HSA] on [Some concepts from] Functions, Algebra, Probability and Data Analysis.

Item. “In a small town, 250 randomly sampled registered voters were asked to state whether they would vote “Yes” or “No” on Measure A in the next local election. The table below shows the results of the survey.

VOTER SURVEY RESULTS

Yes No Undecided

96 34 120

There are 5,500 people expected to vote in the next election. Based on the data, how many people will vote “No” on Measure A in the next election?”

(This is 2007 Public Release Algebra/Data Analysis Item #38 of the Maryland High School Assessment [MD HSA] on [Some concepts from] Functions, Algebra, Probability and Data Analysis at http://mdk12.org/assessments/high_school/look_like/2007/algebra/ftri38.html This is also Item #37 at http://www.mdk12.org/assessments/high_school/look_like/2007/algebra/hsaAlgebra.pdf)

To obtain the expected “correct” answer of 2,112, students are expected to make a number of unwarranted and usually incorrect assumptions. Students who answer 2,112, on a college political science exam will likely be marked wrong.

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