Question
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.
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.
Answers
GPT-4o mini
To create a conditional frequency table based on the preferences for soda or water given the preference for hamburgers or hot dogs, we need to first calculate the conditional percentages for soda and water relative to the total preferences for hamburgers and hot dogs.
Here's the original data from the two-way frequency table:
| | Hamburgers | Hot Dogs | Total |
|-----------|------------|----------|-------|
| **Soda** | 41 | 20 | 61 |
| **Water** | 31 | 28 | 59 |
| **Total** | 72 | 48 | 120 |
Now let's calculate the conditional frequency percentages for soda and water using the total counts for hamburgers and hot dogs.
### Step 1: Calculate the percentages for Hamburgers
- Total hamburgers = 72 (from the table)
- Soda (Hamburgers) = 41
- Water (Hamburgers) = 31
**Conditional Frequencies for Hamburgers:**
- Percentage for Soda:
\[ \text{Percentage of Soda given Hamburgers} = \frac{41}{72} \times 100 \approx 57\% \]
- Percentage for Water:
\[ \text{Percentage of Water given Hamburgers} = \frac{31}{72} \times 100 \approx 43\% \]
### Step 2: Calculate the percentages for Hot Dogs
- Total hot dogs = 48 (from the table)
- Soda (Hot Dogs) = 20
- Water (Hot Dogs) = 28
**Conditional Frequencies for Hot Dogs:**
- Percentage for Soda:
\[ \text{Percentage of Soda given Hot Dogs} = \frac{20}{48} \times 100 \approx 42\% \]
- Percentage for Water:
\[ \text{Percentage of Water given Hot Dogs} = \frac{28}{48} \times 100 \approx 58\% \]
### Step 3: Construct the Conditional Frequency Table
Now we can summarize the findings in a conditional frequency table:
| Preference | Hamburgers (%) | Hot Dogs (%) |
|--------------|----------------|---------------|
| **Soda** | 57 | 42 |
| **Water** | 43 | 58 |
### Final Conditional Frequency Table
Rounded to the nearest whole number:
| Preference | Hamburgers (%) | Hot Dogs (%) |
|--------------|----------------|---------------|
| **Soda** | 57 | 42 |
| **Water** | 43 | 58 |
This table shows the conditional frequency percentages of students who prefer soda or water given their preference for hamburgers or hot dogs.
Here's the original data from the two-way frequency table:
| | Hamburgers | Hot Dogs | Total |
|-----------|------------|----------|-------|
| **Soda** | 41 | 20 | 61 |
| **Water** | 31 | 28 | 59 |
| **Total** | 72 | 48 | 120 |
Now let's calculate the conditional frequency percentages for soda and water using the total counts for hamburgers and hot dogs.
### Step 1: Calculate the percentages for Hamburgers
- Total hamburgers = 72 (from the table)
- Soda (Hamburgers) = 41
- Water (Hamburgers) = 31
**Conditional Frequencies for Hamburgers:**
- Percentage for Soda:
\[ \text{Percentage of Soda given Hamburgers} = \frac{41}{72} \times 100 \approx 57\% \]
- Percentage for Water:
\[ \text{Percentage of Water given Hamburgers} = \frac{31}{72} \times 100 \approx 43\% \]
### Step 2: Calculate the percentages for Hot Dogs
- Total hot dogs = 48 (from the table)
- Soda (Hot Dogs) = 20
- Water (Hot Dogs) = 28
**Conditional Frequencies for Hot Dogs:**
- Percentage for Soda:
\[ \text{Percentage of Soda given Hot Dogs} = \frac{20}{48} \times 100 \approx 42\% \]
- Percentage for Water:
\[ \text{Percentage of Water given Hot Dogs} = \frac{28}{48} \times 100 \approx 58\% \]
### Step 3: Construct the Conditional Frequency Table
Now we can summarize the findings in a conditional frequency table:
| Preference | Hamburgers (%) | Hot Dogs (%) |
|--------------|----------------|---------------|
| **Soda** | 57 | 42 |
| **Water** | 43 | 58 |
### Final Conditional Frequency Table
Rounded to the nearest whole number:
| Preference | Hamburgers (%) | Hot Dogs (%) |
|--------------|----------------|---------------|
| **Soda** | 57 | 42 |
| **Water** | 43 | 58 |
This table shows the conditional frequency percentages of students who prefer soda or water given their preference for hamburgers or hot dogs.