(B) is the correct answer. In the population view, higher education level is correlated, on average, with higher income, but this doesn't apply at the individual level. Indeed, despite the overall population pattern, it would certainly be possible to find someone with a sixth-grade education who struck a fortune and therefore was richer than many people with Ph.D.'s. It wouldn't be likely, if we picked a random person with a sixth-grade education and a random Ph.D., but it would be possible.
(A) plays on the correlation-causality fallacy. Chess is correlated with education level, but doesn't "cause" education level. Education level is correlated with income, but doesn't singlehandedly "cause" income. There is no reason to conclude what (A) says.
(C) plays on the fallacy of scope. Yes, there's a correlation in the overall population, but just because Jane has a Ph.D. and Chris doesn't even have an B.A., we can't automatically assume that Jane is better at chess.
(D) is tricky. The "education level" variable implied the idea of "length of time being educated", but that's not explicitly part of the variable. The question very clearly says one of the last three categories is "Master's Degree", so all master's degree would fall into this category, irrespective of the duration of the program.
(E) also plays on the correlation-causality fallacy. In general, folks who are more proficient at chess are more likely to pursue higher degrees, but it's not that step-by-step in their year-by-year learning process, they are steadily learning more about chess. In other words, the education does not strictly "cause" the proficiency in chess.
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Also It is important to notice:
Correlation does not imply causality. This is tricky, because of course, the inverse is true: causality does, in fact, imply correlation. If A reliably causes B, then whenever you find A, you will be likely to find B. For example, smoking causes a large collection of undesirable conditions, including lung cancer, emphysema, and heart disease, and sure enough, it is highly correlated with each of these.
The catch, though, is that two things can be correlated and A does not cause B. For example, A & B would be highly correlated if they were the common response to the same underlying cause: for example, beer sales and ice cream sales are highly correlated, not because folks like having beer a la mode, but because another cause, hot weather, drives both. There are other more complicated relationships we will not explore here in which A & B would tend to show up together — that is, they would be correlated — but each would not be a relationship in which one is causing the other.
Another way to say this is: correlation is relatively easy to demonstrate. All you need is broad sociological or epidemiological data, and you can show correlation. Anyone with a data set and statistical software can demonstrate correlation. By contrast, demonstrating causality is often a major scientific achievement, sometimes worthy of a Nobel Prize. To demonstrate that A causes B, one would need to show dozens and dozens of conditions are met, only the most elementary of which is that A is correlated with B.