Module 11
Sampling and Conclusion Language.
標本と結論の英語 （Hyōhon to Ketsuron no Eigo）
帰国子女・インターナショナルスクール生のための、デジタルSAT 数学の無料教材。独学で進められます。
These questions test one idea: how far a conclusion may travel from the data. Three limits matter.
- Who was studied? A conclusion may only be extended to the population that was actually sampled.
- Was it random? Without random selection, results do not generalise beyond the people surveyed.
- Association or cause? A survey or observational study supports "is associated with", never "causes". Only a randomised experiment supports cause.
日本人がハマる理由
この形式の問題で選択肢を分けているのは、suggests、is associated with、likely、may のように言い切らない語と、proves、causes、all、exactly のように言い切る語の対立です。英語を第二言語として読んでいると、各選択肢の話題をつかみ、話題の合うものを選んでしまいます。しかし試されているのは動詞の強さです。日本語では「〜かもしれない」「〜と考えられる」のように結論の強さが文末に出ますが、英語ではそれが文の途中の動詞に出るため、読み飛ばしやすいのです。この種の問題では、どの選択肢も話題は同じで、違うのは modality（断定の強さ）だけです。動詞に線を引いてください。
練習問題
難易度は出題者による目安です。College Board の判定ではありません。
A researcher surveyed 200 randomly selected students at Lincoln High School and found that 62% of them prefer online homework to paper homework. Which conclusion is best supported by these results?
Correct Answer: C
Explanation: The sample was random and drawn from Lincoln High School, so the conclusion may extend to that school and no further. 62% is a majority, which supports "most".
- (A): Extends beyond the sampled population. Students at one school cannot represent the country.
- (B): "Exactly" is too strong. A sample estimates the true percentage; it does not pin it down precisely.
- (D): Introduces performance, which was never measured, and claims causation from a preference survey.
Difficulty Justification
Rated Medium. All four choices concern the same survey; they differ only in how far each one travels from it.
A study of 1,000 students found that those who ate breakfast scored higher on a standardised test than those who did not. Which conclusion is best supported?
Correct Answer: A
Explanation: The study observed a difference between two existing groups; students were not randomly assigned to eat breakfast. That supports association only.
- (B): Claims causation from an observational study. Some other factor — household routine, sleep, income — could produce both.
- (C): Reverses the causal direction, and is equally unsupported.
- (D): Contradicts the data, which did show a difference.
Difficulty Justification
Rated Medium. Choice B is what the finding feels like it means. The rule is absolute: no random assignment, no causal claim.
A researcher surveyed adults at a science museum about their interest in scientific topics and found a high level of interest. Why might these results not generalise to all adults in the city?
Correct Answer: B
Explanation: People who choose to visit a science museum are already more likely to be interested in science. The sample is biased by self-selection, so it cannot represent all adults however large it becomes.
- (A): No sample size was given, and size is not the problem here — a biased sample of 100,000 museum visitors would be just as unrepresentative.
- (C): The number of questions does not affect who was sampled.
- (D): Irrelevant, and percentages on a multi-topic survey need not total 100%.
Difficulty Justification
Rated Hard. "Sample too small" is the reflexive answer, and on generalisation questions like this one it is almost always wrong — the flaw is who was sampled, not how many.
But do not over-learn that. Sample size genuinely is the answer on a different subtype: when a question asks about the margin of error or the precision of an estimate, a larger sample narrows the interval. Read which is being asked — can this conclusion travel? (→ who was sampled) or how precise is this number? (→ how many).