To correctly describe the category variables for a two-way table representing the data given, let's break down the information:
- Total Babies Born: 160
- Girls: \( \frac{3}{5} \) of 160 = 96 girls (since \( \frac{3}{5} \times 160 = 96 \))
- Boys: \( 160 - 96 = 64 \) boys
- Babies Weighing 8 Pounds or More: 70 babies
- 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:
-
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. -
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. -
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