Question
The city of Hamden received money for improvements of the town’s park. The park committee polled a random sample of 75 residents from the town. Of the 75 residents, 27 would like to see more trees planted in the park. From this information, what can be inferred?
Most residents in the town would like to have more trees in the park.
Exactly 36% of the residents in the town would like more trees in the park.
About a third of the residents prefer a park improvement of more trees.
Residents who use the park the most would like more trees planted.
Most residents in the town would like to have more trees in the park.
Exactly 36% of the residents in the town would like more trees in the park.
About a third of the residents prefer a park improvement of more trees.
Residents who use the park the most would like more trees planted.
Answers
GPT-4o mini
From the information provided, we can infer the following:
- **Exactly 36% of the residents in the town would like more trees in the park.** This is true mathematically since 27 out of 75 residents corresponds to the proportion of 27/75, which simplifies to 0.36 or 36%. However, this does not necessarily reflect the entire population of the town unless the sample is representative.
- **About a third of the residents prefer a park improvement of more trees.** This is a reasonable inference based on the sample size of 75 residents, where 36% approximately aligns with a third.
The other two statements, "Most residents in the town would like to have more trees in the park," and "Residents who use the park the most would like more trees planted," cannot be logically inferred from the sample polling alone. The sample size is not representative of the entire population without further context, and preferences based on usage are not mentioned in the data.
So, the best inferences are:
1. About a third of the residents prefer a park improvement of more trees.
2. It is also true that exactly 36% of the surveyed residents would like more trees, but this is contingent on the survey's sample being representative of the whole town.
- **Exactly 36% of the residents in the town would like more trees in the park.** This is true mathematically since 27 out of 75 residents corresponds to the proportion of 27/75, which simplifies to 0.36 or 36%. However, this does not necessarily reflect the entire population of the town unless the sample is representative.
- **About a third of the residents prefer a park improvement of more trees.** This is a reasonable inference based on the sample size of 75 residents, where 36% approximately aligns with a third.
The other two statements, "Most residents in the town would like to have more trees in the park," and "Residents who use the park the most would like more trees planted," cannot be logically inferred from the sample polling alone. The sample size is not representative of the entire population without further context, and preferences based on usage are not mentioned in the data.
So, the best inferences are:
1. About a third of the residents prefer a park improvement of more trees.
2. It is also true that exactly 36% of the surveyed residents would like more trees, but this is contingent on the survey's sample being representative of the whole town.