Question 16·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A sports-drink company set up a booth at the finish line of a local marathon. The next 150 runners who crossed the finish line were asked to taste both the original drink and a new flavor and then choose which flavor they preferred. Of the runners surveyed, 84% chose the new flavor.
Which conclusion is most reasonably supported by these data?
For SAT statistics questions about conclusions, always start by identifying exactly who was studied and what the numbers say about that group. Then, check which answer choice matches that specific group and describes the result (like a majority) correctly, without stretching to a larger or different population that the sample does not represent. If an answer talks about a much broader group than the one in the study, it is usually not supported by the data.
Hints
Focus on the group described in the setup
Reread the first two sentences. Who exactly tasted the drinks and gave their preference? Be precise about that group.
Think about what “most” means
The problem says 84% chose the new flavor. How does 84% compare to half of the group? What word do we use when more than half of a group has some preference?
Be careful about generalizing
Ask yourself: Are these 150 marathon finishers guaranteed to represent all runners in the country, all customers of the company, or all spectators? Which answer choice keeps the conclusion limited to the people who were actually surveyed?
Desmos Guide
Confirm that 84% means “most” of the 150 runners
In Desmos, type 0.84 * 150 to see how many of the 150 runners preferred the new flavor. Then compare this number to to confirm that it is more than half of the group, which supports a statement that “most” of the surveyed runners preferred the new flavor.
Step-by-step Explanation
Identify who was actually surveyed
Read the setup carefully. Only the next 150 runners who crossed the finish line at this local marathon were asked to taste both drinks and choose a favorite.
So the data describe:
- People who finished this particular marathon
- Who agreed to taste both samples
- And then stated which flavor they preferred
No other people (spectators, other customers, runners in other places) were surveyed.
Interpret the percentage
Of the runners surveyed, 84% chose the new flavor.
- "Most" means more than 50%.
- Since is clearly more than , we know that a majority of the surveyed runners preferred the new flavor.
So any reasonable conclusion must say that among the specific group that was surveyed, most preferred the new flavor.
Decide how far you can generalize
In statistics, you can only generalize from a sample to a larger group if the sample is representative of that larger group.
Here, the sample is a convenience sample: runners at the finish line of one local marathon. That is not a random sample of:
- All long-distance runners in the country
- All customers of the company
- All spectators at the race
So any answer that makes a claim about those larger groups goes beyond what the data support.
Match the supported conclusion to the answer choices
We need the choice that:
- Talks about this specific marathon’s finishers who tried both samples (the actual group studied), and
- States that most of them preferred the new flavor (because ).
The only option that does this—without making claims about any bigger or different group—is:
D) Most runners who finished this particular marathon and tried both samples preferred the new flavor.