A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students' accuracy...

1. TRANSLATE the study setup

• Given information:
  • Random sample of 35 students
  • Sample drawn from: "all students at one middle school"
  • Study found significant improvement in fraction accuracy
  • Need to find: largest group for generalization

2. INFER the generalization principle

• Key insight: Study results can only be generalized to the population from which the random sample was originally drawn
• This protects against over-generalizing findings beyond what the data actually supports

3. INFER the correct scope

• The sample came from "all students at one middle school"
• Therefore, results can be generalized to all students at that same school
• Cannot generalize beyond this because the sample wasn't drawn from those broader populations

Answer: B. All students at the school

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students think "bigger is better" and assume results can be generalized to the largest possible group mentioned in the answer choices.

They reason: "If the game works for middle school students, it should work for all middle school students in the city, or even all students in the city." This ignores the fundamental limitation that you can only generalize to the population you actually sampled from.

This may lead them to select Choice C (All middle school students in the city) or Choice D (All students in the city).

Second Most Common Error:

Conceptual confusion about generalization: Students think generalization means "applies only to the exact sample studied" rather than understanding it extends to the broader population that was sampled.

They reason: "We only studied 35 students, so we can only say something about those 35 students." This misses that random sampling allows generalization to the entire population from which the sample was drawn.

This may lead them to select Choice A (The 35 students in the sample).

The Bottom Line:

This problem tests understanding of a fundamental research principle: random sampling allows generalization, but only to the population that was actually sampled from, not to any broader group the researcher didn't sample.