To calculate the conditional relative frequencies for students who prefer sprinkles or jelly beans, given they prefer chocolate or vanilla, we will create a two-way table that focuses on the preferences within each ice cream flavor category (Vanilla and Chocolate).
First, we need to calculate the relative frequencies (in percentage) for each topping within the Vanilla and Chocolate categories. The formula to find the conditional relative frequency is:
\[ \text{Conditional Relative Frequency} = \left(\frac{\text{Frequency of topping for a given flavor}}{\text{Total for that flavor}}\right) \times 100 \]
For Vanilla:
- Total for Vanilla = 175
- Sprinkles = 102
- Jelly Beans = 73
Calculating the conditional relative frequencies:
- Sprinkles (Vanilla): \[ \left(\frac{102}{175}\right) \times 100 \approx 58.3% \quad \text{(rounds to 58%)} \]
- Jelly Beans (Vanilla): \[ \left(\frac{73}{175}\right) \times 100 \approx 41.7% \quad \text{(rounds to 42%)} \]
For Chocolate:
- Total for Chocolate = 190
- Sprinkles = 65
- Jelly Beans = 125
Calculating the conditional relative frequencies:
- Sprinkles (Chocolate): \[ \left(\frac{65}{190}\right) \times 100 \approx 34.2% \quad \text{(rounds to 34%)} \]
- Jelly Beans (Chocolate): \[ \left(\frac{125}{190}\right) \times 100 \approx 65.8% \quad \text{(rounds to 66%)} \]
Conditional Relative Frequency Table:
Putting everything together gives us the final two-way table of conditional relative frequencies:
| | Sprinkles (%) | Jelly Beans (%) | |------------|---------------|-----------------| | Vanilla | 58 | 42 | | Chocolate | 34 | 66 |
Thus the final answer is:
- Vanilla: Sprinkles = 58%, Jelly Beans = 42%
- Chocolate: Sprinkles = 34%, Jelly Beans = 66%