Question
Last July, 160 babies were born in a hospital in Maine; 3
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more. If that data was represented in a two-way table, which of the following could correctly describe the category variables?
Column: Boys, Less Than 8 Pounds; Row: Girls, 8 Pounds or More
Column: Boys, 8 Pounds or More; Row: Girls, Less Than 8 Pounds
Column: Less Than 8 Pounds, 8 Pounds or More; Row: Boys, Girls
5
of the babies were girls. Seventy babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more. If that data was represented in a two-way table, which of the following could correctly describe the category variables?
Column: Boys, Less Than 8 Pounds; Row: Girls, 8 Pounds or More
Column: Boys, 8 Pounds or More; Row: Girls, Less Than 8 Pounds
Column: Less Than 8 Pounds, 8 Pounds or More; Row: Boys, Girls
Answers
GPT-4o mini
To correctly describe the category variables for a two-way table representing the data given, let's break down the information:
1. **Total Babies Born**: 160
2. **Girls**: \( \frac{3}{5} \) of 160 = 96 girls (since \( \frac{3}{5} \times 160 = 96 \))
3. **Boys**: \( 160 - 96 = 64 \) boys
4. **Babies Weighing 8 Pounds or More**: 70 babies
5. **Boys Weighing 8 Pounds or More**: 50 boys
From this data, we can summarize the number of babies based on weight and gender:
- Total girls: 96
- Total boys: 64
- Boys weighing 8 pounds or more: 50
- Therefore, boys weighing less than 8 pounds = \( 64 - 50 = 14 \)
- Total babies weighing 8 pounds or more: 70
- Thus, girls weighing 8 pounds or more = \( 70 - 50 = 20 \)
- Girls weighing less than 8 pounds = \( 96 - 20 = 76 \)
Now, we need to determine the category variables for the two-way table. Here are the options:
1. **Column: Boys, Less Than 8 Pounds; Row: Girls, 8 Pounds or More**
This does not correctly represent the data because it mixes weight categories for boys with a specific category for girls.
2. **Column: Boys, 8 Pounds or More; Row: Girls, Less Than 8 Pounds**
This categorizes boys by whether they weigh 8 pounds or more, but relates to girls' weight as less than 8 pounds, which is not a balanced representation of all categories.
3. **Column: Less Than 8 Pounds, 8 Pounds or More; Row: Boys, Girls**
This option organizes the table by weight categories (less than 8 pounds and 8 pounds or more) for both boys and girls, which appropriately summarizes the distinct categories.
Therefore, the correct representation of the category variables for the two-way table is:
**Column: Less Than 8 Pounds, 8 Pounds or More; Row: Boys, Girls**
1. **Total Babies Born**: 160
2. **Girls**: \( \frac{3}{5} \) of 160 = 96 girls (since \( \frac{3}{5} \times 160 = 96 \))
3. **Boys**: \( 160 - 96 = 64 \) boys
4. **Babies Weighing 8 Pounds or More**: 70 babies
5. **Boys Weighing 8 Pounds or More**: 50 boys
From this data, we can summarize the number of babies based on weight and gender:
- Total girls: 96
- Total boys: 64
- Boys weighing 8 pounds or more: 50
- Therefore, boys weighing less than 8 pounds = \( 64 - 50 = 14 \)
- Total babies weighing 8 pounds or more: 70
- Thus, girls weighing 8 pounds or more = \( 70 - 50 = 20 \)
- Girls weighing less than 8 pounds = \( 96 - 20 = 76 \)
Now, we need to determine the category variables for the two-way table. Here are the options:
1. **Column: Boys, Less Than 8 Pounds; Row: Girls, 8 Pounds or More**
This does not correctly represent the data because it mixes weight categories for boys with a specific category for girls.
2. **Column: Boys, 8 Pounds or More; Row: Girls, Less Than 8 Pounds**
This categorizes boys by whether they weigh 8 pounds or more, but relates to girls' weight as less than 8 pounds, which is not a balanced representation of all categories.
3. **Column: Less Than 8 Pounds, 8 Pounds or More; Row: Boys, Girls**
This option organizes the table by weight categories (less than 8 pounds and 8 pounds or more) for both boys and girls, which appropriately summarizes the distinct categories.
Therefore, the correct representation of the category variables for the two-way table is:
**Column: Less Than 8 Pounds, 8 Pounds or More; Row: Boys, Girls**