Question 47·Medium·Evaluate Statistical Claims: Observational Studies and Experiments
A researcher wants to investigate whether taking a daily vitamin supplement affects sleep quality. The researcher recruits 600 adult volunteers and asks each one whether they already take a daily vitamin supplement. The 280 volunteers who report taking the supplement average 7.2 hours of sleep per night, and the 320 volunteers who do not take the supplement average 6.8 hours of sleep per night.
Which of the following conclusions is best supported by the results of this study?
For questions about what conclusions are supported by a study, first identify whether the study is experimental (researcher assigns treatments randomly) or observational (researcher only measures existing differences). If it's observational, rule out any answer that says one variable causes another, predicts what would happen under a change, or makes strong statements about all people based on a single sample. Then use the actual numbers given (like the group averages and their difference) to choose the option that simply and accurately describes the results for the participants in the study without overreaching.
Hints
Think about how the data were collected
Did the researcher assign some volunteers to start taking vitamins and others not to, or did the researcher just ask what they already do? Decide if this is an experiment or an observational study.
Check for cause-and-effect language
Look at which answer choices use words like "causes" or "would increase." Ask yourself: from an observational study, are you allowed to make a cause-and-effect claim or a prediction about what will happen if someone changes behavior?
Sample versus all adults
The study includes 600 adult volunteers. Is that the same as all adults? Which answer choices jump from describing these volunteers to making a statement about every adult?
Use the given averages carefully
The two groups average 7.2 and 6.8 hours of sleep. Which choice simply restates the difference between these two averages for the people in the study, without claiming anything extra?
Desmos Guide
Confirm the difference in averages
In Desmos, type 7.2 - 6.8 into an expression line and look at the output. This value is the difference in average nightly sleep between the two groups in the study; use it to identify which answer choice correctly describes that difference without making extra claims about causation or all adults.
Step-by-step Explanation
Identify the type of study
Read carefully how the data were collected: the researcher asks each volunteer whether they already take a daily vitamin supplement. The researcher does not assign people to start or stop taking vitamins.
That means this is an observational study, not a randomized experiment. In an observational study, people already have their own habits; the researcher just records them.
Recall what conclusions observational studies allow
From an observational study:
- We can describe patterns in the sample (for example, compare averages between groups).
- We cannot confidently say that one variable causes changes in another, because there could be other differences between the groups (like stress, diet, health, work schedule, etc.).
- We also should be careful about making strong claims about all adults based on a single group of 600 volunteers, especially if they were not randomly selected from all adults.
Compute and interpret the difference in averages
The problem gives two averages:
- Vitamin group: hours per night
- No-vitamin group: hours per night
Find the difference:
So, within this study, the vitamin group slept on average hour more per night than the non-vitamin group. This is a description of the sample, not proof of cause-and-effect.
Match the safe conclusion to the answer choices
Now eliminate answer choices that claim too much:
- Any choice that says the supplement "causes" more sleep goes beyond what an observational study can show.
- Any choice that talks about "all adults" or what "would" happen if people started taking vitamins is also too strong.
The only acceptable conclusion is the one that:
- Stays within these 600 volunteers, and
- Simply reports that the group who reported taking vitamins slept, on average, hour longer per night than the group who did not.
That statement is: "Among the 600 volunteers in this study, the participants who reported taking a daily vitamin supplement slept, on average, 0.4 hour longer per night than those who did not."