Question 19·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A technology company surveyed 250 runners who had completed at least one marathon in the past year. The runners were asked whether they regularly use the company’s new running app. Of the runners surveyed, 72% said yes.
Which of the following conclusions is supported by the results of the survey?
For survey and statistics interpretation questions, first lock in who was actually surveyed and exactly what was measured. Then, for each answer choice, ask: (1) Is it talking about the same population as the survey or is it expanding to a broader/different group (like all people, all exercisers, or people not surveyed)? and (2) Does it match what the numbers allow us to say (for example, recognizing that percentages above 50% support words like "most"). Eliminate any statement that goes beyond the data or refers to a group we have no information about.
Hints
Focus on the group being described
Underline the description of the people who were actually surveyed. Then check which answer choices are talking about that same group and which ones are expanding to different groups.
Think about what 72% means
Compare 72% to 50%. What does it mean about a group if more than half of its members have a certain characteristic?
Watch out for overgeneralizations
Ask yourself for each choice: does this claim go beyond the specific runners who were surveyed, such as talking about all marathoners, all exercisers, or runners who were never in the survey at all?
Desmos Guide
Compute how many runners use the app
In Desmos, type 0.72*250 to see how many of the 250 surveyed runners reported using the app. This helps you understand the size of the group using the app.
Compare to half the group
In Desmos, type 0.5*250 to find half of 250, and compare that result to 0.72*250. Use this comparison to decide whether more than half of the surveyed runners use the app, then choose the answer choice that talks about this same surveyed group and reflects that majority.
Step-by-step Explanation
Identify who was actually surveyed
Carefully read the first sentence: the company surveyed 250 runners who had completed at least one marathon in the past year.
That means all the data we have comes only from this specific group:
- They are runners.
- They completed at least one marathon.
- They did so in the past year.
We do not have any data about:
- All marathon runners ever.
- All people who exercise.
- People who have never run a marathon.
Interpret the 72% figure
The problem says that 72% of these 250 runners said they regularly use the app.
You can also convert this to a count:
So about 180 out of 250 surveyed runners use the app.
Compare 72% to 50%:
- 50% would be half the group.
- 72% is greater than 50%.
So more than half of the surveyed runners use the app.
Check which answer choices match the surveyed group
Now examine what each option is claiming about who the statement is about:
- Choice A: "all people who run marathons" – this is a much larger group than the surveyed 250.
- Choice B: "all people who exercise regularly" – this includes many people who are not marathon runners; we did not survey them.
- Choice C: "runners who have never run a marathon" – this is the opposite type of group from the one surveyed.
- Choice D: "runners who completed a marathon in the past year" – this matches the description of the surveyed runners.
Only one choice talks about the same type of runners as in the survey and just summarizes that a majority of them use the app.
Select the supported conclusion
From the survey, we know that 72% (more than half) of the runners who completed a marathon in the past year use the app. Saying that most runners who completed a marathon in the past year regularly use the app is exactly what the data supports without stretching to a broader or different group, so that is the supported conclusion.