Question

decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). explain your reasoning. our total class score is based only on homework and exams, and i have better scores than you on both homework and exams. therefore, i have a better overall score than you. choose the correct answer below. a. the statement does not make sense, because it is possible to appear better in each of two or more group comparisons but still be equal overall because of how the data are divided into equally - sized groups. b. the statement makes sense, because it is not possible to appear better in each of two or more group comparisons but still be worse overall. c. the statement makes sense, because homework and exams are weighted equally. d. the statement does not make sense, because it is possible to appear better in each of two or more group comparisons but still be worse overall because of how the data are divided into unequally - sized groups.

Explanation:

This is related to Simpson's paradox. Simpson's paradox shows that when data is divided into unequally - sized groups, a trend can be reversed when the groups are combined. Just because someone has better scores in each category (homework and exams), if the weights (sizes) of these categories are different in an overall score calculation (unequally - sized groups in data terms), the overall score may not be better. For example, if homework is a small part of the grade and exams are a large part, and the person with better scores in each has a very small advantage in homework but a small disadvantage in exams (because of the unequal weight of the two components), the overall score could be worse.

Answer:

D. The statement does not make sense, because it is possible to appear better in each of two or more group comparisons but still be worse overall because of how the data are divided into unequally - sized groups.