Question 8·Medium·Evaluate Statistical Claims: Observational Studies and Experiments
Researchers at River City High School wanted to investigate whether there is a relationship between how much seniors sleep on school nights and their performance on the ACT® exam. They selected a simple random sample of 350 seniors and recorded each student’s average hours of sleep per school night and ACT composite score.
In the sample, the mean ACT score was 25.3 for the 148 students who reported sleeping at least 8 hours per school night and 22.1 for the 202 students who reported sleeping fewer than 8 hours.
Which of the following conclusions is best supported by the study’s design and the observed results?
For questions about interpreting study results, first identify whether the study is an experiment (with random assignment) or an observational study. Remember: random assignment allows causal conclusions; random sampling allows you to generalize to the population sampled from. Then scan answer choices for overly strong language like “causes,” “exactly,” “all,” or “must,” and eliminate any claims that go beyond what the design and data can support, keeping only those that talk about an appropriate level of certainty (usually an association within the correct population).
Hints
Think about how the data were collected
Did the researchers assign students to sleep at least 8 hours or fewer than 8 hours, or did they simply record what students already did? How does that affect what you can conclude?
Association vs. causation
From an observational study, what kind of link between two variables can you claim? Are you allowed to say that one variable causes changes in the other?
Watch for overly strong wording
Look for words like “exactly,” “causes,” or “must” in the answer choices. Do the data and study design really justify such strong claims?
Desmos Guide
Check the size of the difference in means
In Desmos, type 25.3 - 22.1 to see the numerical difference between the sample mean ACT scores for the two sleep groups. Use this as a sense of how large the observed difference is, then think about whether the study’s observational design justifies causal language or exact population claims.
Step-by-step Explanation
Understand what the study actually did
Researchers took a simple random sample of 350 seniors from River City High School. For each student, they recorded (did not assign) two variables:
- Average hours of sleep per school night (at least 8 vs. fewer than 8)
- ACT composite score
They found that the sample mean ACT score was 25.3 for the “at least 8 hours” group and 22.1 for the “fewer than 8 hours” group, a difference of 3.2 points in the sample.
Identify the study type and what it allows you to conclude
Because the researchers only observed students’ existing sleep habits and did not randomly assign students to different sleep amounts, this is an observational study, not an experiment.
From an observational study:
- You can talk about a relationship/association between variables.
- You cannot claim that one variable causes changes in the other, because there may be other differences between the groups (like stress, study habits, health, etc.).
Decide which population you can talk about
The sample was a simple random sample of seniors at River City High School.
With a simple random sample, you can usually generalize patterns from the sample to the population it was drawn from (here, all seniors at that school), but:
- You still expect sampling variability, so the true difference in the population is unlikely to be exactly the sample difference of 3.2.
- Strong words like “exactly,” “must,” or definite causal language go beyond what the data and design justify.
Evaluate each answer choice against the design and data
Now check each statement:
- Choice A says the average difference for all seniors is exactly 3.2 points. The 3.2-point gap is from the sample; the true population difference might be close but is almost never known to be exactly the same.
- Choice B uses causal language (“causes” and “scores to increase”). Because this is an observational study (no random assignment), we cannot say that more sleep causes higher ACT scores.
- Choice D says the difference must have been due solely to random variation. The data show a fairly large difference; the design does not force us to conclude it’s only random noise.
The only remaining option is the one that:
- Describes a relationship between sleep and ACT score (not cause-and-effect), and
- Stays within the population of seniors at River City High School, without claiming an exact numerical difference for all.
That option is: Among seniors at River City High School, there is an association between average nightly sleep and ACT score.