A survey of alumni of the class of 1960 at Aurora University yielded puzzling results. When asked to indicate their a...

odsimkins June 17, 2020

Why A not E?

HI -- I read the explanation in the other thread about why A is right but what's confusing to me is that when expalinining, the writer seemed to act as though A said half of the high-ranking alumni responded to the survey. Why are we to assume that a disproportionately alrge number means half, or...can you explain why A is better than E in a different way? I chose E because it says "academic rank at Aurrora was based on a number of consideratios in addition to average grades" and because the stimulus says, "when asked to indicate their academic rank, half of the respondents reported that they were in the top quarter of the graduating class," and I took top quarter of gradating class to mean top quarter in terms of academic ranking. Could you explain?

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shunhe June 18, 2020

Hi @odsimkins,

Thanks for the question! So we have here a survey where over half the 1960 alumni respondents indicated they were in the top quarter of the graduating class. And we have to resolve this paradox. First, anticipating some possible answers, one possibility immediately jumps into mind: some of them are lying! Of course, this isn’t an answer choice, so we might want to think of another possibility. And that possibility is: this is a survey, which means that it’s not necessarily the case that everyone answered the survey. Let’s say there are 100 total alumni in the class of 1960, but only 50 responded to the survey. And of those 50, it just happens that everyone in the top quarter responded to the survey (maybe they felt a closer connection to the school since they did so well). Well, then 25/50 respondents to the survey (half the respondents) would have said they were in the top quarter. But that’s only because not everyone responded to the survey; the top quarter was 100% represented, and the rest of the class was only 25/75 = 33% represented. This is the possibility that (A) presents; a disproportionately large number of high-ranking alumni responded to the survey.

(E), on the other hand, doesn’t help because it doesn’t matter what’s calculated into academic rank; the fact remains that the survey is about academic rank (regardless of what’s counted into it). The survey asks them to indicate their academic rank, not just their grades. So the paradox can’t be resolved by changing around what defines academic rank.

Hope this helps! Feel free to ask any other questions that you might have.