A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia...

1. TRANSLATE the sampling information

• Given information:
  • Organizer selected 55 teams at random from all trivia teams in the tournament
  • Table shows data for 40 teams that practiced \(\geq 3\) hours per week
  • Four answer choices about different populations

2. INFER the key statistical principle

• The crucial insight: When determining generalization scope, focus on the original sampling method, not the data presented
• Random sampling allows generalization back to the original population
• The sampling frame was 'all trivia teams in the tournament'

3. INFER why the table subset doesn't matter

• The table shows only 40 teams (those practicing \(\geq 3\) hours), but this is just a subset of the data
• The original sample of 55 teams was still drawn randomly from all tournament teams
• Generalization scope depends on where the sample came from, not which data gets displayed

4. Apply the generalization principle

• Since sample was drawn from 'all trivia teams in the tournament'
• Results can be generalized to 'all trivia teams in the tournament'
• This matches Choice D

Answer: D. All trivia teams in the tournament

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students focus on the 40 teams shown in the table instead of the original sampling method. They think, 'The study only shows data for 40 teams who practiced at least 3 hours, so results only apply to teams like these.' This surface-level reading misses that generalization depends on the original sampling frame (all tournament teams), not the subset of data presented.

This may lead them to select Choice C (The 40 trivia teams in the sample that practiced for at least 3 hours per week)

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret what constitutes the 'population' by focusing on the sample itself rather than where it came from. They think the 55 sampled teams are the population of interest, missing that these teams represent a broader group.

This may lead them to select Choice B (The 55 trivia teams in the sample)

The Bottom Line:

This problem tests whether students understand that statistical generalization depends on sampling method, not data presentation. The table is a red herring - what matters is that teams were randomly selected from all tournament teams.