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.
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
To evaluate whether the student's sample is appropriate and a good representation of the population, let's consider a few factors:
1. **Random Selection**: The student is testing ice samples from randomly selected cups of water. If the cups were chosen randomly and represent different times, customers, or types of beverages served at the local restaurant, then this aspect seems appropriate.
2. **Sample Size**: The student is testing 15 samples. While this number can give some insight, it might be considered relatively small depending on the volume of ice being made in the restaurant and the variety of sources from which ice is drawn.
3. **Representation of the Population**: To determine whether the sample represents the entire population of ice produced by the restaurant, it depends on the variety of cups selected. If the random samples come from various times of the day or various drinks served, it can reflect the overall quality of the ice more accurately.
Considering all these points:
- If the random selection captures different aspects of the ice usage in the restaurant, then it is reasonable to conclude that the sample could be appropriate and representative.
- If the sample is biased (e.g., all from the same time slot or only from the same type of water source), then it would not accurately represent the ice the restaurant serves.
Given that we do not have complete information about the randomness of selection and homogeneity of the ice production process, we would lean towards:
**Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.**
This conclusion assumes there could be variability in the ice quality or contamination that a small sample size may not capture adequately. However, if more detailed information suggests the sample was diverse and representative, reassessment may be warranted.
1. **Random Selection**: The student is testing ice samples from randomly selected cups of water. If the cups were chosen randomly and represent different times, customers, or types of beverages served at the local restaurant, then this aspect seems appropriate.
2. **Sample Size**: The student is testing 15 samples. While this number can give some insight, it might be considered relatively small depending on the volume of ice being made in the restaurant and the variety of sources from which ice is drawn.
3. **Representation of the Population**: To determine whether the sample represents the entire population of ice produced by the restaurant, it depends on the variety of cups selected. If the random samples come from various times of the day or various drinks served, it can reflect the overall quality of the ice more accurately.
Considering all these points:
- If the random selection captures different aspects of the ice usage in the restaurant, then it is reasonable to conclude that the sample could be appropriate and representative.
- If the sample is biased (e.g., all from the same time slot or only from the same type of water source), then it would not accurately represent the ice the restaurant serves.
Given that we do not have complete information about the randomness of selection and homogeneity of the ice production process, we would lean towards:
**Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.**
This conclusion assumes there could be variability in the ice quality or contamination that a small sample size may not capture adequately. However, if more detailed information suggests the sample was diverse and representative, reassessment may be warranted.