Question 7·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A university committee wants to estimate the percentage of all students who support extending library hours. The committee emails an online poll to 800 students who have checked out a book from the library in the past month. Of the 640 students who respond, 90% indicate they favor extended hours.
Which statement about this study is most accurate?
For SAT statistics questions about surveys and experiments, first identify the population of interest (who we care about) and the sample (who was actually studied). Ask if the sample is randomly chosen from the whole population or if it overrepresents a particular group—that’s selection bias. Then check whether answer choices talk about response rate, sample size, or generalizing results, and pick the one that correctly describes the main flaw or limitation in the study design.
Hints
Focus on who was surveyed
Look carefully at which students were emailed the poll. Are they a random mix of all students, or do they share something in common?
Compare the sample to the population of interest
The question is about all students at the university. Does the group that was surveyed truly represent every type of student, including those who never or rarely use the library?
Check what each choice is claiming
Some choices talk about representativeness, some about what the survey "demonstrates," and some about response rate. Think about which issue is actually the biggest problem in this study's design.
Step-by-step Explanation
Understand what the study is trying to estimate
The committee wants to estimate the percentage of all students at the university who support extending library hours. That means the sample should represent the entire student population, not just a specific subgroup with special interest in the library.
Examine how the sample was chosen
The committee emailed a poll to 800 students who have checked out a book from the library in the past month, and 640 of them responded. This is not a random sample of all students; it's a sample only from recent library users, who are more likely than other students to care about library hours. This creates sampling bias (also called selection bias), because one group is overrepresented.
Match the study issue to the correct statement
Now compare each answer choice to the situation:
- A high response rate alone does not guarantee that the sample represents all students if the original group was biased.
- The survey results (90% in favor) apply only to the group surveyed, not automatically to all students.
- The main flaw is that only recent library users were sampled, which likely makes the results biased.
- The number of responses (640) is not the source of bias here; the way the sample was selected is.
Therefore, the most accurate statement is: The results are likely biased because the sample includes only students who recently used the library.