Let's analyze the problem step by step:
1. Population Identification:
The population in a statistical study refers to the entire group that the researcher is interested in. In this case, Bart is interested in the sandwich preferences of all his customers.
- So, the population consists of all customers.
2. Sample Identification:
The sample is the subset of the population that is actually surveyed or studied. Bart surveyed a few of his friends who have eaten at his food truck.
- Thus, the sample consists of the friends who responded.
3. Conclusion from the Survey:
Based on the survey results, we need to determine the majority preference among Bart's friends. According to the data:
```
Friends Preferring Grilled Sandwiches: 15
Friends Preferring Plain Sandwiches: 5
```
The majority, which is 15 out of 20 respondents, prefer grilled sandwiches.
- Therefore, it can be concluded that most of Bart's friends prefer grilled sandwiches.
4. Improving Accuracy:
To improve the accuracy of the results, Bart should consider surveying a larger and more representative sample. Ideally, he should survey a wider range of his actual customers rather than just his friends.
- The results would have been more accurate if Bart had surveyed more people, preferably a random sample of his actual customers.
With these points in mind, let's fill in the blanks in the statement:
- Population: all customers
- Sample: the friends who responded
- Conclusion: most of Bart's friends prefer grilled sandwiches
- Accuracy Improvement: more people, preferably a random sample of his actual customers
Final statement:
"In this case, the population consists of all customers and the sample consists of the friends who responded. Based on the results, it can be concluded that most of Bart's friends prefer grilled sandwiches. The results would have been more accurate if Bart had surveyed more people, preferably a random sample of his actual customers."
