Question 13·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
To learn how students feel about a new healthy-lunch menu, a school principal placed a comment box next to the salad bar in the cafeteria. Over one week, 120 students left comments, and 95 of those comments were positive.
Which of the following best describes the principal’s method for gathering data?
For questions about surveys and experiments, first identify the population (who we care about) and the sample (who was actually measured). Then check if the sampling method gives every member of the population a roughly equal chance to be included; if not, the sample is biased. Be careful not to blame sample size when the real issue is the way participants were chosen, and always match your reasoning (bias, randomness, representativeness) directly to the wording of the answer choices.
Hints
Focus on who was surveyed
Look carefully at where the comment box was placed and think about which students would be most likely to see and use it.
Population vs. sample
Compare the group that left comments to all students in the school. Are these two groups likely to have similar opinions?
Sample size vs. sampling method
Decide whether the main issue is how many students were surveyed or which students were surveyed.
Eliminate extreme or irrelevant options
Check which choices talk about drawing conclusions, which talk about where the sample came from, and which suggest a different group to survey. Which type of issue actually fits this situation?
Desmos Guide
Compute the proportion of positive comments
Type 95/120 into Desmos to see the decimal value and percentage of positive comments among the students who left comments.
Interpret the result in context
Look at the proportion you found and ask yourself: does a high proportion within this subgroup (students who used the salad bar and left comments) guarantee that the same proportion holds for all students in the school, or could the way the sample was collected affect the result?
Step-by-step Explanation
Identify the population and the sample
The population is all students in the school. The sample is the 120 students who chose to leave comments in a box located next to the salad bar.
Ask if every student had an equal chance to be in the sample
Only students who go to the salad bar could easily see and use the comment box. Students who skip the salad bar or don’t eat in the cafeteria probably had little or no chance to leave a comment. This makes the sample a convenience sample, not a random sample.
Think about how the sampling location could affect opinions
Students who choose food from the salad bar are more likely to like healthy options than students who avoid it. So the group that left comments is probably more positive about the healthy menu than the average student in the school.
Match this idea to the answer choices
The key issue is not the number of comments but that the sample is not representative of all students, because it mainly includes salad-bar users who may already favor healthy food. Therefore, the best description is: “The sampling method is biased because students who use the salad bar may be more likely to favor healthy food.”