Question
The school cafeteria conducted a survey of randomly selected middle school students to determine students' favorite lunches. The table shows the results of the survey.
Favorite Lunches
Entrée Number of Students
Chicken nuggets 33
Hamburger 42
Hot dog 22
Pizza 50
Spaghetti 27
Tacos 22
Other 4
Which inferences about all middle school students at this school appears to be valid?
(choose 2)
Responses
A Students are less likely to select a tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.Students are less likely to select a tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.
B More students would select pizza or spaghetti as their favorite lunch than any other two entrées.More students would select pizza or spaghetti as their favorite lunch than any other two entrées.
C Students are less likely to select a hamburger as their favorite lunch that a hot dog or tacos as their favorite lunch.Students are less likely to select a hamburger as their favorite lunch that a hot dog or tacos as their favorite lunch.
D Half the students are likely to select pizza as their favorite lunch.Half the students are likely to select pizza as their favorite lunch.
E Students are more likely to select a hamburger or hot dogs as their favorite lunch than pizza or spaghetti as their favorite lunch.
Favorite Lunches
Entrée Number of Students
Chicken nuggets 33
Hamburger 42
Hot dog 22
Pizza 50
Spaghetti 27
Tacos 22
Other 4
Which inferences about all middle school students at this school appears to be valid?
(choose 2)
Responses
A Students are less likely to select a tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.Students are less likely to select a tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.
B More students would select pizza or spaghetti as their favorite lunch than any other two entrées.More students would select pizza or spaghetti as their favorite lunch than any other two entrées.
C Students are less likely to select a hamburger as their favorite lunch that a hot dog or tacos as their favorite lunch.Students are less likely to select a hamburger as their favorite lunch that a hot dog or tacos as their favorite lunch.
D Half the students are likely to select pizza as their favorite lunch.Half the students are likely to select pizza as their favorite lunch.
E Students are more likely to select a hamburger or hot dogs as their favorite lunch than pizza or spaghetti as their favorite lunch.
Answers
GPT-4o mini
Based on the data provided from the survey of middle school students' favorite lunches, we can evaluate the options:
- **A:** Students are less likely to select tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.
- Valid, because pizza (50) is the most popular choice, while tacos (22) and chicken nuggets (33) are less than pizza.
- **B:** More students would select pizza or spaghetti as their favorite lunch than any other two entrées.
- Valid, since pizza (50) + spaghetti (27) = 77, which is more than the highest other combination (hamburger (42) + chicken nuggets (33) = 75).
- **C:** Students are less likely to select a hamburger as their favorite lunch than a hot dog or tacos as their favorite lunch.
- Invalid because the number of students selecting hamburgers (42) is more than both hot dogs (22) and tacos (22).
- **D:** Half the students are likely to select pizza as their favorite lunch.
- Invalid if we consider half of the total responses. The total number of surveyed students is 33 + 42 + 22 + 50 + 27 + 22 + 4 = 200, so half would be 100. Since 50 students selected pizza, this doesn’t represent half.
- **E:** Students are more likely to select a hamburger or hot dogs as their favorite lunch than pizza or spaghetti as their favorite lunch.
- Invalid because the sum for hamburgers (42) + hot dogs (22) = 64, which is less than the total for pizza (50) + spaghetti (27) = 77.
Thus, the two valid inferences are:
- **A:** Students are less likely to select tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.
- **B:** More students would select pizza or spaghetti as their favorite lunch than any other two entrées.
- **A:** Students are less likely to select tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.
- Valid, because pizza (50) is the most popular choice, while tacos (22) and chicken nuggets (33) are less than pizza.
- **B:** More students would select pizza or spaghetti as their favorite lunch than any other two entrées.
- Valid, since pizza (50) + spaghetti (27) = 77, which is more than the highest other combination (hamburger (42) + chicken nuggets (33) = 75).
- **C:** Students are less likely to select a hamburger as their favorite lunch than a hot dog or tacos as their favorite lunch.
- Invalid because the number of students selecting hamburgers (42) is more than both hot dogs (22) and tacos (22).
- **D:** Half the students are likely to select pizza as their favorite lunch.
- Invalid if we consider half of the total responses. The total number of surveyed students is 33 + 42 + 22 + 50 + 27 + 22 + 4 = 200, so half would be 100. Since 50 students selected pizza, this doesn’t represent half.
- **E:** Students are more likely to select a hamburger or hot dogs as their favorite lunch than pizza or spaghetti as their favorite lunch.
- Invalid because the sum for hamburgers (42) + hot dogs (22) = 64, which is less than the total for pizza (50) + spaghetti (27) = 77.
Thus, the two valid inferences are:
- **A:** Students are less likely to select tacos or chicken nuggets as their favorite lunch than pizza as their favorite lunch.
- **B:** More students would select pizza or spaghetti as their favorite lunch than any other two entrées.