To find the conditional relative frequency of students who prefer hot dogs given that they prefer soda, we need to follow these steps:
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Identify the given numbers:
- Students who prefer soda: 41
- Students who prefer hot dogs: 28
- Total number of students: \(31 + 41 + 20 + 28 = 120\)
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Conditional relative frequency calculation:
- We need to find out how many of the students who prefer soda also prefer hot dogs. However, we don't have a direct number from your data because we need a little more information about the overlap between those who prefer soda and hot dogs.
Assuming we look at the total number of students preferring hot dogs out of those who prefer soda based on the initial information provided, we don't have specific overlap numbers. In this case, if we could assume an even distribution or lack of any specific preference data regarding combines preferences, we cannot define the answer directly without those figures.
If we were to hypothetically assume that we had data showing all soda drinkers prefer hamburgers, which would make our conditional relative frequency irrelevant as \(0\), or that all drinkers prefer hot dogs, \(28/41\) would be our reference point.
- Calculate the conditional relative frequency once you have the number of soda drinkers who like hot dogs (let's denote this as \( x \)): \[ \text{Conditional relative frequency} = \frac{x}{41} \times 100 \]
Finally, please provide data regarding how many soda drinkers like hot dogs to get a conclusive answer or check if overall preferences in a study reflect specific compositions. If you do not have that data, we can conclude with the base figures provided.