Question 1·Easy·Evaluate Statistical Claims: Observational Studies and Experiments
A nutritionist surveyed 150 randomly selected adults who reported exercising at least 5 days each week. Each participant was asked which post-workout snack they preferred: a protein bar or a piece of fruit. In the survey, 120 of the 150 respondents (80%) said they preferred fruit.
Which of the following inferences is most supported by the survey result?
For survey and experiment inference questions, first underline who was actually studied and how they were selected. You can usually generalize only to the larger group that matches the sample description (for example, all people with a certain characteristic) and only if the sample was random from that group. Then check that the answer choice talks about that same population, not a broader or different one, and that the strength of the claim matches the data (sample percentages justify words like "most," not exact numbers or claims about groups that were never observed). Discard any option that changes the group, adds new conditions, or makes a stronger claim than the data support.
Hints
Focus on the sampled group
Look closely at the phrase that describes who was surveyed. Does every adult have this characteristic, or just a certain subset of adults?
Think about what you can generalize to
In statistics, you can generalize from a random sample to the larger population that sample represents. Which answer choices talk about that same population, and which ones talk about a different or larger group?
Match the wording to the data
The survey result is that 80% of the sample preferred fruit. Does this support a statement about an exact percentage, or is a more general phrase (like something that just indicates it is more than half) more appropriate?
Desmos Guide
Verify the sample proportion
Type 120/150 into Desmos and note the decimal output; then convert that to a percentage. Compare this percentage to 50% to confirm that the survey shows a clear majority of the sampled group prefers fruit, which supports a general "most"-type claim (not an exact percentage) about the same population described in the prompt.
Step-by-step Explanation
Identify who was surveyed
Carefully read the description of the sample: 150 randomly selected adults who reported exercising at least 5 days each week. That means every person in the survey belongs to this specific group of adults who exercise frequently.
Identify what was measured
Each participant was asked which post-workout snack they preferred: a protein bar or a piece of fruit. The result was that 120 out of 150, or , said they preferred fruit.
Decide what population we can generalize to
Because the adults were randomly selected from the group of adults who exercise at least 5 days a week, we can use the survey to make an inference about all adults who exercise at least 5 days a week. We cannot safely extend conclusions to all adults, all gym members, or adults with different exercise habits.
Match the strength of the claim to the data
A sample percentage of supports a general statement like "most" for that population, but not an exact percentage for everyone. So we should:
- Reject any choice that talks about all adults or all gym members instead of adults who exercise at least 5 days a week.
- Reject any choice that claims exactly 80% of some whole population.
- Reject any choice that talks about people who do not exercise at least 5 days a week, because the study never surveyed them. The only option that correctly limits the conclusion to adults who exercise at least 5 days a week and uses an appropriate word like "most" is: Most adults who exercise at least 5 days a week prefer fruit to protein bars as a post-workout snack.