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

1 answer

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