Evaluating Statistical Claims Pattern - Pinpoint the Population

Identifying the population a sample was drawn from to determine generalizability

These questions describe a study with a random sample and ask: "To which group can the findings be generalized?" The answer is always the specific population from which the sample was randomly drawn — no broader, no narrower.

The Core Rule

A random sample allows you to generalize to the population it was drawn from — and only that population.

• Too broad: Extending results to a larger group (all students vs. biology seniors).
• Too narrow: Limiting results to only the sample itself (the 150 people surveyed).
• Just right: The exact population described in the sampling sentence.

How to Find the Right Answer

Look for the sentence that says "randomly selected [number] from [population]." The bracketed population is your answer. Everything else — the survey topic, the results, the percentages — is irrelevant to the generalizability question.

Example — Easy

A park ranger randomly selected $120$ hikers from a registry of hikers who completed the Granite Loop Trail last year. Of those surveyed, $78\%$ said they preferred a new map design. Which inference can appropriately be drawn?

A) At least 78% of all visitors to the national park will prefer the new map.
B) Most people who completed the Granite Loop Trail last year will prefer the new map.
C) At least 78% of first-time hikers at the park will prefer the new map.
D) Most people who disliked the previous map will not prefer the new map.

The sample was drawn from hikers who completed the Granite Loop Trail last year.
78% preferred the new map → most of that population likely would too.
Answer: B

Choice A extends to all park visitors (too broad). Choice C extends to first-time hikers (different group). Choice D makes a claim about a group defined by preference, which was never sampled.

Example — Hard (Multiple Qualifiers)

An educational researcher randomly selected $300$ students from all 10th-grade students in a large urban school district who had an average grade of B in their previous year's math courses. These students used a new learning platform for one semester. To what group can the results most reliably be applied?

A) All 10th-graders in the district who used the platform for one semester.
B) The 300 students selected for the study.
C) All 10th-grade students in the district.
D) All 10th-graders in the district who had an average grade of B in their previous year's math courses.

The population has three qualifiers: 10th-grade, in the district, B average in math.
Answer: D

Choice A adds a condition (used the platform) that came from the experiment, not the sampling frame. Choice B is just the sample — too narrow. Choice C drops the "B average" qualifier — too broad.

Common Traps

• Confusing experimental conditions with sampling criteria. If the study lasted 16 weeks or used a new tool, those are things done to the sample — they don't define the population.
• Choosing the sample itself. If 120 people were surveyed, the answer is almost never "the 120 people." A random sample is meant to represent the larger group.
• Dropping a qualifier. If the population is "marathon runners in Texas who completed at least three marathons," dropping "at least three marathons" makes the answer too broad.

What to Do on Test Day

• Find the sampling sentence — it always says "randomly selected [N] from [population]." Underline the population.
• Match every qualifier. The correct answer will include all the criteria in the sampling sentence — grade level, location, specific behavior, etc.
• Ignore everything after the sampling. What the participants did during the study (used a platform, took a test) doesn't change who they represent.
• The answer is never the sample itself unless the study used no random selection (which would be a different pattern).