Question
The food service manager conducted a random survey of students to determine their preference for new lunch menu items. Select all the inferences that can be drawn from the manager’s data.
Item Number of
Students
Pizza 6
Salad Bar 27
Pita Sandwiches 13
Burritos 24
About twice as many students prefer salad bar as compared to pita sandwiches.
Burritos are the most preferred item.
About three-fourths of students prefer either salad bar or burritos.
Twice as many students prefer pizza as compared to pita sandwiches.
About half as many students prefer pita sandwiches as compared to burritos.
Item Number of
Students
Pizza 6
Salad Bar 27
Pita Sandwiches 13
Burritos 24
About twice as many students prefer salad bar as compared to pita sandwiches.
Burritos are the most preferred item.
About three-fourths of students prefer either salad bar or burritos.
Twice as many students prefer pizza as compared to pita sandwiches.
About half as many students prefer pita sandwiches as compared to burritos.
Answers
GPT-4o mini
To evaluate the inferences based on the provided data, we can summarize the number of students who prefer each item:
- Pizza: 6
- Salad Bar: 27
- Pita Sandwiches: 13
- Burritos: 24
Now let's analyze each of the inferences made:
1. **About twice as many students prefer salad bar as compared to pita sandwiches.**
- Salad Bar: 27 students
- Pita Sandwiches: 13 students
- Twice as many would be approximately 26. Since 27 is close to 26, this statement is **true**.
2. **Burritos are the most preferred item.**
- Burritos: 24 students
- Salad Bar: 27 students
- The salad bar is preferred by more students than the burritos, so this statement is **false**.
3. **About three-fourths of students prefer either salad bar or burritos.**
- Total preferences = 6 + 27 + 13 + 24 = 70
- Salad Bar + Burritos = 27 + 24 = 51
- Three-fourths of 70 is 52.5. Since 51 is not around 52.5, this statement is **false**.
4. **Twice as many students prefer pizza as compared to pita sandwiches.**
- Pizza: 6 students
- Pita Sandwiches: 13 students
- Twice as many would be 26, which is not close to 6 (6 is less than 13). Therefore, this statement is **false**.
5. **About half as many students prefer pita sandwiches as compared to burritos.**
- Pita Sandwiches: 13 students
- Burritos: 24 students
- Half of 24 is 12; since 13 is close to 12, this statement is **true**.
Based on the evaluation, the following inferences can be drawn:
- **True:**
- About twice as many students prefer salad bar as compared to pita sandwiches.
- About half as many students prefer pita sandwiches as compared to burritos.
- **False:**
- Burritos are the most preferred item.
- About three-fourths of students prefer either salad bar or burritos.
- Twice as many students prefer pizza as compared to pita sandwiches.
In summary, the correct inferences are that about twice as many students prefer salad bar as compared to pita sandwiches, and about half as many students prefer pita sandwiches as compared to burritos.
- Pizza: 6
- Salad Bar: 27
- Pita Sandwiches: 13
- Burritos: 24
Now let's analyze each of the inferences made:
1. **About twice as many students prefer salad bar as compared to pita sandwiches.**
- Salad Bar: 27 students
- Pita Sandwiches: 13 students
- Twice as many would be approximately 26. Since 27 is close to 26, this statement is **true**.
2. **Burritos are the most preferred item.**
- Burritos: 24 students
- Salad Bar: 27 students
- The salad bar is preferred by more students than the burritos, so this statement is **false**.
3. **About three-fourths of students prefer either salad bar or burritos.**
- Total preferences = 6 + 27 + 13 + 24 = 70
- Salad Bar + Burritos = 27 + 24 = 51
- Three-fourths of 70 is 52.5. Since 51 is not around 52.5, this statement is **false**.
4. **Twice as many students prefer pizza as compared to pita sandwiches.**
- Pizza: 6 students
- Pita Sandwiches: 13 students
- Twice as many would be 26, which is not close to 6 (6 is less than 13). Therefore, this statement is **false**.
5. **About half as many students prefer pita sandwiches as compared to burritos.**
- Pita Sandwiches: 13 students
- Burritos: 24 students
- Half of 24 is 12; since 13 is close to 12, this statement is **true**.
Based on the evaluation, the following inferences can be drawn:
- **True:**
- About twice as many students prefer salad bar as compared to pita sandwiches.
- About half as many students prefer pita sandwiches as compared to burritos.
- **False:**
- Burritos are the most preferred item.
- About three-fourths of students prefer either salad bar or burritos.
- Twice as many students prefer pizza as compared to pita sandwiches.
In summary, the correct inferences are that about twice as many students prefer salad bar as compared to pita sandwiches, and about half as many students prefer pita sandwiches as compared to burritos.