Hamburgers Hot Dogs Total

Soda 41 20 61
Water 31 28 59
Total 72 48 120
Use the two-way frequency table to complete the conditional frequency table for students who prefer soda or water given they prefer hamburgers or hot dogs. Round each percentage to the nearest whole number.

(1 point)
Hamburgers (%) Hot Dogs(%) Total(%)
Soda
%
% 100
Water 53 47 100

1 answer

To complete the conditional frequency table for students who prefer soda or water given they prefer hamburgers or hot dogs, we will calculate the percentage for soda among hamburgers and hot dogs based on the totals for those categories.

Step 1: Calculate the total number of students who prefer each food item

From the original table:

  • Total students who prefer hamburgers = 72
  • Total students who prefer hot dogs = 48

Step 2: Calculate the percentage for Soda

For Hamburgers:

  • Students who prefer soda and hamburgers = 41
  • Percentage of students who prefer soda and hamburgers = (41 / 72) * 100

\[ \text{Percentage of Soda (Hamburgers)} = \left( \frac{41}{72} \right) \times 100 \approx 56.94 \approx 57% \]

For Hot Dogs:

  • Students who prefer soda and hot dogs = 20
  • Percentage of students who prefer soda and hot dogs = (20 / 48) * 100

\[ \text{Percentage of Soda (Hot Dogs)} = \left( \frac{20}{48} \right) \times 100 \approx 41.67 \approx 42% \]

Step 3: Complete the Conditional Frequency Table

Now, we can fill in the conditional frequency table:

 	Hamburgers (%)	Hot Dogs(%)	Total(%)
Soda	57              42              100
Water	53              47              100

Final Conditional Frequency Table:

 	Hamburgers (%)	Hot Dogs (%)	Total (%)
Soda	57              42              100
Water	53              47              100

So the completed conditional frequency table is:

  • Soda (Hamburgers) = 57%
  • Soda (Hot Dogs) = 42%
  • Water (Hamburgers) = 53%
  • Water (Hot Dogs) = 47%

This result is consistent with the requirement to round the percentages to the nearest whole number.