Question
For a biology project, a student wants to research whether the ice at a local restaurant is clean and free from impurities. She decides to test 15 ice samples from randomly selected cups of water.
Determine whether her sample is an appropriate, random sample and a good representation of the population.
Option #1: Yes, her sample is an appropriate, random sample. It is a good representation of the population.
Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.
Answers
GPT-4o mini
The correct response would depend on a few additional factors regarding how the student collected her samples. Generally, here are considerations for evaluating whether the sample is appropriate and representative:
1. **Method of Selection**: If the 15 samples were selected randomly from different cups of water at the restaurant (e.g., from various times of day, different drinks, or different servers), it strengthens the argument that it is a random sample.
2. **Sample Size**: A sample size of 15 can be adequate, but it's small relative to the entire population of ice served at the restaurant. However, if the samples are collected correctly, it may still offer insights.
3. **Variability in Ice Quality**: If the ice produced and served in the restaurant is relatively homogeneous (e.g., made from the same source of water and prepared in the same way), then a sample from different cups might be sufficient. However, if there are significant differences in ice quality due to different production methods or water sources, a random sample from only 15 cups may not accurately reflect the whole population.
4. **Target Population**: The student should define what population she is representing. Is it all ice produced by the restaurant, or just the ice in the cups she sampled?
Taking all this into account, without specific details on how the samples were chosen, it's difficult to definitively label the sample as appropriate. However, based on the limited information provided, I would lean towards:
**Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.**
This is primarily because a sample of 15 from potentially different sources and variability might not capture the overall quality of all the ice produced or served by the restaurant.
1. **Method of Selection**: If the 15 samples were selected randomly from different cups of water at the restaurant (e.g., from various times of day, different drinks, or different servers), it strengthens the argument that it is a random sample.
2. **Sample Size**: A sample size of 15 can be adequate, but it's small relative to the entire population of ice served at the restaurant. However, if the samples are collected correctly, it may still offer insights.
3. **Variability in Ice Quality**: If the ice produced and served in the restaurant is relatively homogeneous (e.g., made from the same source of water and prepared in the same way), then a sample from different cups might be sufficient. However, if there are significant differences in ice quality due to different production methods or water sources, a random sample from only 15 cups may not accurately reflect the whole population.
4. **Target Population**: The student should define what population she is representing. Is it all ice produced by the restaurant, or just the ice in the cups she sampled?
Taking all this into account, without specific details on how the samples were chosen, it's difficult to definitively label the sample as appropriate. However, based on the limited information provided, I would lean towards:
**Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.**
This is primarily because a sample of 15 from potentially different sources and variability might not capture the overall quality of all the ice produced or served by the restaurant.