To determine which category has an error in the table, we need to verify if the given conditions match the data presented. Let's go through each condition step-by-step:
### Condition 1: Breakfast Preference
- Given Condition: Breakfast is preferred by one and a half times more children than adults.
- Table Data:
- Children preferring breakfast: 30
- Adults preferring breakfast: 45
#### Calculation:
According to the condition, the number of children preferring breakfast should be 1.5 times the number of adults.
[tex]\[ \text{Expected children preferring breakfast} = 1.5 \times \text{Adults preferring breakfast} \][/tex]
[tex]\[ \text{Expected children preferring breakfast} = 1.5 \times 45 = 67.5 \][/tex]
However, according to the table:
[tex]\[ \text{Actual children preferring breakfast} = 30 \][/tex]
Since 30 does not equal 67.5, there is a discrepancy in the breakfast category.
### Condition 2: Dinner Preference
- Given Condition: Children and adults both had 24 respondents for dinner.
- Table Data:
- Children preferring dinner: 24
- Adults preferring dinner: 24
#### Verification:
Since both the given condition and the table data have 24 respondents for dinner by both children and adults, there is no error in the dinner category.
### Condition 3: Lunch Preference
- Given Condition: There were 62 adults who responded lunch, twice as great as the number of children who responded lunch.
- Table Data:
- Children preferring lunch: 31
- Adults preferring lunch: 62
#### Calculation:
According to the condition, the number of adults preferring lunch should be twice the number of children.
[tex]\[ \text{Expected children preferring lunch} = \frac{\text{Adults preferring lunch}}{2} \][/tex]
[tex]\[ \text{Expected children preferring lunch} = \frac{62}{2} = 31 \][/tex]
According to the table:
[tex]\[ \text{Actual children preferring lunch} = 31 \][/tex]
Since 31 matches 31, there is no error in the lunch category.
### Conclusion
There is a discrepancy between the given condition and the table data in the breakfast category. Thus, the category that has an error in the table is:
Breakfast
