To complete the conditional frequency table based on the given two-way frequency table, we'll calculate the percentages of students who prefer soda or water given their preference for hamburgers or hot dogs.
We first identify the total number of responses within each category (Hamburgers and Hot Dogs) and then compute the conditional percentages for each beverage preference.
Here is the summary table with preference counts:
| | Hamburgers | Hot Dogs | Total | |----------------------|------------|----------|-------| | Soda | 41 | 20 | 61 | | Water | 31 | 28 | 59 | | Total | 72 | 48 | 120 |
Step 1: Calculate Percentages Given Hamburgers
- For those who prefer Hamburgers:
- Total = 72
- Soda = 41 → \( \frac{41}{72} \times 100 \approx 57% \)
- Water = 31 → \( \frac{31}{72} \times 100 \approx 43% \)
Step 2: Calculate Percentages Given Hot Dogs
- For those who prefer Hot Dogs:
- Total = 48
- Soda = 20 → \( \frac{20}{48} \times 100 \approx 42% \)
- Water = 28 → \( \frac{28}{48} \times 100 \approx 58% \)
Final Conditional Frequency Table
Now, we can create the conditional frequency table based on the calculations:
| | Prefer Soda | Prefer Water | Total | |------------------|-------------|--------------|-------| | Prefer Hamburgers | 57% | 43% | 100% | | Prefer Hot Dogs | 42% | 58% | 100% |
This table represents the conditional preferences of students who prefer soda or water given whether they prefer hamburgers or hot dogs, with percentages rounded to the nearest whole number.