Bunuel wrote:

Political Analyst: Polling suggests that the Labour candidate will win the upcoming election. She only trails her opponent by one percentage point among male voters, but her strong favorability with women has her leading by three full percentage points among female voters.

Which of the following, if true, would most call the argument above into question?

A. Polls are not always accurate predictors of election outcomes.

B. Female voters make up less than one quarter of all voters.

C. It is not uncommon for voters to change their minds even within minutes of casting their votes.

D. Not everyone in the electorate has taken part in the referenced polls.

E. Labour candidates have traditionally been unsuccessful with this electorate.

VERITAS PREP OFFICIAL SOLUTION:

Whenever Critical Reasoning problems involve statistics it's a good idea to look at those statistics with a skeptical eye. Here you're told that, in the polls, the Labour candidate has a 3% advantage with women and a 1% disadvantage with men, and that leads to the conclusion that the polls suggest she will win.

But remember - a classic data flaw is that of the imbalanced groups (the classic "more people die in their beds each year than by climbing Mount Everest, so therefore it's safer to climb Everest than to take a nap?" fallacy where way almost everyone at some point lays in a bed but virtually no one climbs Mount Everest). What if, in this particular electorate, there were just way, way more males than females?

Choice (B), the correct answer, addresses that. If females are less than 1/4 of the electorate, then the three points she gains with females is fewer votes than the point she loses with males. To prove this you could set up the math as:

M > 3F (the ratio of M:F is greater than 3:1)

Then if she has a 3% advantage in the number of females but a 1% deficit in the number of males, she's looking at a total advantage of:

3F - 1M

Where, if M >3F, that becomes: 3F - (>3)F

So her advantage is negative. For that reason (B) is correct, as it shows that a 3% advantage among females is not enough to suggest an overall advantage.

Among the other choices, note the analyst's exact conclusion, that "polling suggests that the Labour candidate will win." She isn't quite claiming that the candidate will win, but instead concluding that the polling suggests that she will win. That renders tempting choices (A), (C), and (D) incorrect: with this specific conclusion it doesn't matter if the polls directly connect to a win, just that they suggest a win. Similarly (D) is irrelevant, as this conclusion isn't about historical context, but rather what these polls say about this particular election.

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