Question 34·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A student newspaper interviewed 150 students at Central High School who reported that they participate in at least one after-school sport. Each of these students was asked how many hours they typically sleep on school nights, and 72% said they sleep at least 8 hours per night.
Which of the following inferences can appropriately be drawn from this survey result?
For survey and statistics questions, always start by identifying exactly who was surveyed (the sample) and what larger group they represent (the population). Then check whether each answer choice stays within that population or improperly jumps to a different group (such as all students, another subgroup, or a comparison between groups when only one group was measured). Eliminate any choice that goes beyond the data collected or tries to make a comparison or cause-and-effect claim the study design does not support.
Hints
Focus on who was included in the survey
Look carefully at the description of the 150 students. Were they a random mix of all students, or did they share a specific characteristic?
Focus on what the 72% describes
The 72% comes from the answers of the 150 surveyed students. Ask yourself: 72% of which group exactly?
Notice what groups are missing
Did the survey collect any information from students who do not participate in after-school sports? Could the survey show how those students compare to sports participants?
Eliminate overreaching conclusions
Cross out any answer that makes a claim about a group that was not actually surveyed or tries to compare two groups when data were only collected on one group.
Desmos Guide
Interpret the 72% using a quick calculation (optional)
In Desmos, type 0.72 * 150 to see how many of the 150 surveyed sports-participating students reported sleeping at least 8 hours. Use this to reinforce that the 72% refers only to the surveyed sports participants, not to other students.
Step-by-step Explanation
Identify who was surveyed
Read the first sentence carefully: "150 students at Central High School who reported that they participate in at least one after-school sport".
This means every student in the survey is a sports participant. No non-sports students were surveyed.
Identify what was measured
Each of these 150 sports-participating students was asked how many hours they typically sleep on school nights.
We are told that 72% of these students (the surveyed sports participants) said they sleep at least 8 hours per night.
So the 72% is a percentage of the surveyed sports participants only.
Decide what population this sample can represent
Because the sample consisted only of students who participate in at least one after-school sport at Central High School, the best we can do is use this sample to estimate something about all sports-participating students at that school.
We cannot make claims about:
- all students at the school (sports and non-sports together), or
- students who do not participate in sports, or
- comparisons between sports and non-sports students,
because those groups were either not fully represented or not included at all in the survey.
Match this to the answer choices
Now match this logic to the options:
- Any statement about all students at the school goes beyond the surveyed group.
- Any statement about non-sports students is impossible here because we have no data on them.
- Any statement comparing sports vs. non-sports sleep amounts is also impossible with only one group.
The only appropriate inference is the one that limits the conclusion to students who participate in after-school sports at Central High School and states that about 72% of them sleep at least 8 hours per night.