Question 46·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A school newspaper wants to estimate the proportion of all students at a large high school who regularly read for pleasure. To collect data, reporters posted a link to a survey on the school's book club social media page and received 120 responses; 85% of respondents said they regularly read for pleasure.
Which statement best evaluates the claim that about 85% of all students at the school regularly read for pleasure?
For SAT questions about evaluating statistical claims, focus first on how the sample was chosen, not just the number of responses or the technology used. Ask: Did every member of the population have a fair, roughly equal chance of being selected (random, representative sample), or is it a convenience or self-selected sample likely to be biased? Be skeptical of choices that (1) rely only on sample size, (2) make extreme claims like "always" or "never," or (3) incorrectly say that methods like social media automatically give every person an equal chance. Choose the option that correctly identifies whether the sample is representative of the population being described.
Hints
Focus on how the sample was collected
Look closely at where the survey link was posted. Who is most likely to see and answer that survey?
Think about representativeness
Ask yourself: Are students who follow the book club social media page typical of all students at the school in terms of reading habits?
Be careful with extreme or irrelevant reasoning
Check each answer: Does it rely on an extreme statement like "always" or ignore how the sample was chosen? Or does it correctly talk about whether this particular sample represents the whole school?
Step-by-step Explanation
Identify what is being claimed
The newspaper is using the survey result to claim that about 85% of all students at the school regularly read for pleasure. The key question is whether this survey result is a good estimate of the true proportion for all students.
Examine how the data were collected
The survey link was posted on the school's book club social media page, and students chose whether or not to respond. This creates two issues:
- The people who see the survey are likely in or following the book club, which is a group especially interested in reading.
- The survey is voluntary (self-selected): only students who decide to respond are included.
Both of these make it unlikely that the sample represents the entire student body.
Decide whether the sample is representative
A good estimate for the whole school needs a sample where all students have a fair chance of being selected (for example, a random sample from the entire student list). Here, students who are not in the book club or who don’t follow the book club page are very unlikely to be in the sample, even though they are part of the school.
Because the sample overrepresents students who already like books, the sample is biased and probably overestimates the true proportion of students who read for pleasure.
Evaluate each answer choice using this idea
Now compare the choices to this reasoning:
- One choice says the claim is accurate just because there are 120 responses, ignoring that how the sample was collected matters.
- Another choice blames all online surveys in a very extreme way, which is not correct.
- Another claims social media posting gives everyone an equal chance, which is not true here because only book club followers really see it.
- The remaining choice points out that the sample is self-selected from students especially interested in books and therefore is not representative of all students.
The statement that correctly explains why the claim is likely inaccurate is choice C: "The claim is likely inaccurate because the sample is self-selected from students interested in books and is not representative of all students."