Question 10·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A science teacher surveyed 150 students who were members of their school's sports teams. Each student was asked whether they regularly drank energy drinks before practice or games, and 72% of the students answered "Yes."
Which of the following inferences is best supported by the survey results?
For SAT questions about surveys and inferences, first identify the sample (who was actually surveyed) and what was measured. Then decide what population you can reasonably generalize to—usually, you are limited to groups similar to the sample, not to all students or all teenagers. Be on guard against choices that (1) extend conclusions to a much larger or different group than the one surveyed, or (2) claim that one variable causes another when the study only observed what people do. Finally, connect percentages to words like "most" (more than half) or "about" to see which choice accurately matches the data without overreaching.
Hints
Focus on the sample
Reread the first sentence: exactly which students were included in the survey? Were they all students at the school, or a specific subgroup?
Think about generalizing the results
Ask yourself: Is it reasonable to use information from this one group of 150 students to make claims about all students at the school or all teenagers in the country?
Notice what was and wasn’t measured
The survey asked whether students regularly drank energy drinks before practice or games. Did the survey measure athletic performance or compare it between different groups in a controlled way?
Connect the percentage to the word "most"
Since 72% of the surveyed students answered "Yes," think about what that says about how many in that group drink energy drinks compared to half of them.
Desmos Guide
Compute how many students said "Yes"
In Desmos, type 0.72*150 and press Enter. The output tells you how many of the 150 surveyed sports-team students reported regularly drinking energy drinks.
Compare to half the sample
Type 150/2 in Desmos and compare this value to the result of 0.72*150. Notice that the number of "Yes" responses is greater than half of 150, which corresponds to interpreting the percentage as a majority of the surveyed group.
Step-by-step Explanation
Identify who was actually surveyed
Carefully read the description of the sample: the teacher surveyed 150 students who were members of their school's sports teams. That means:
- The data come only from students on sports teams.
- The survey does not include non-athlete students or teenagers from other schools or areas.
Understand what the survey measured
Each of these 150 students was asked whether they regularly drank energy drinks before practice or games, and 72% answered "Yes."
- Converting 72% to a decimal gives .
- If you multiply , you get the number of surveyed students who said "Yes."
- Since 72% is greater than 50%, more than half of the surveyed sports-team students reported regularly drinking energy drinks.
Decide how far the results can be generalized
On SAT statistics questions, you can only generalize to groups similar to the sample.
- Because only sports-team students at one school were surveyed, the results cannot support statements about:
- All high school students at the school (this would include many students who were not surveyed).
- All teenagers in the country (this is far beyond the surveyed group).
- Also, the question only asked what students do, not how well they perform, so it tells you nothing about whether energy drinks improve performance.
Match the supported inference to the answer choices
Now check each choice:
- (A) talks about most high school students at the school, which goes beyond the sports-team group that was actually surveyed.
- (C) talks about all teenagers in the country, which is an even bigger group and clearly not justified by one school's survey.
- (D) claims that energy drinks improve athletic performance, but the survey did not test performance at all, so this is a causal claim that is unsupported.
The only option that stays within the surveyed group and simply reflects that a majority of them said "Yes" is:
B) Most students who participate on the school's sports teams drink energy drinks.