Question
The owner of an ice cream shop surveyed 350 kids and 600 adults on their topping preferences when buying ice cream. She groups the participants by age group and topping preference. The results of the survey are in the two-way table below. Make a relative frequency table, then determine if there is evidence of an association between the two variables, age group and topping preference.
Start by making a relative frequency table. What percentage of kids surveyed prefer sprinkles?
Prefer
sprinkles Prefer
cookie dough Total
Kids 112 238 350
Adults 192 408 600
Total 304 646 950
Relative frequency table
Prefer
sprinkles Prefer
cookie dough Total
Kids
%
Adults
Start by making a relative frequency table. What percentage of kids surveyed prefer sprinkles?
Prefer
sprinkles Prefer
cookie dough Total
Kids 112 238 350
Adults 192 408 600
Total 304 646 950
Relative frequency table
Prefer
sprinkles Prefer
cookie dough Total
Kids
%
Adults
Answers
GPT-4o mini
To create a relative frequency table, we first need to calculate the relative frequencies based on the total number of participants in each age group.
The relative frequency for each category is computed by dividing the count of each category by the total for that row.
**Step 1: Calculate the relative frequencies.**
1. **Kids:**
- Prefer sprinkles: \( \frac{112}{350} \)
- Prefer cookie dough: \( \frac{238}{350} \)
2. **Adults:**
- Prefer sprinkles: \( \frac{192}{600} \)
- Prefer cookie dough: \( \frac{408}{600} \)
**Step 2: Compute the relative frequencies.**
- For Kids:
- Prefer sprinkles:
\[
\frac{112}{350} \approx 0.32 \quad (\text{or } 32\%)
\]
- Prefer cookie dough:
\[
\frac{238}{350} \approx 0.68 \quad (\text{or } 68\%)
\]
- For Adults:
- Prefer sprinkles:
\[
\frac{192}{600} \approx 0.32 \quad (\text{or } 32\%)
\]
- Prefer cookie dough:
\[
\frac{408}{600} \approx 0.68 \quad (\text{or } 68\%)
\]
**Step 3: Fill in the relative frequency table.**
\[
\begin{array}{|c|c|c|c|}
\hline
\textbf{Age Group} & \textbf{Prefer Sprinkles (\%)} & \textbf{Prefer Cookie Dough (\%)} & \textbf{Total} \\
\hline
\text{Kids} & 32\% & 68\% & 100\% \\
\hline
\text{Adults} & 32\% & 68\% & 100\% \\
\hline
\end{array}
\]
**Step 4: Determine if there is an association.**
To determine whether there is an association between age group and topping preference, we can examine the relative frequencies for both groups. Since the percentages for preferring sprinkles and cookie dough are the same for kids and adults (32% prefer sprinkles in both groups), there does not appear to be an association based on topping preferences.
**Conclusion:**
- The percentage of kids surveyed that prefer sprinkles is **32%**.
- There is no evidence of an association between age group and topping preference, as the preferences are the same across both groups.
The relative frequency for each category is computed by dividing the count of each category by the total for that row.
**Step 1: Calculate the relative frequencies.**
1. **Kids:**
- Prefer sprinkles: \( \frac{112}{350} \)
- Prefer cookie dough: \( \frac{238}{350} \)
2. **Adults:**
- Prefer sprinkles: \( \frac{192}{600} \)
- Prefer cookie dough: \( \frac{408}{600} \)
**Step 2: Compute the relative frequencies.**
- For Kids:
- Prefer sprinkles:
\[
\frac{112}{350} \approx 0.32 \quad (\text{or } 32\%)
\]
- Prefer cookie dough:
\[
\frac{238}{350} \approx 0.68 \quad (\text{or } 68\%)
\]
- For Adults:
- Prefer sprinkles:
\[
\frac{192}{600} \approx 0.32 \quad (\text{or } 32\%)
\]
- Prefer cookie dough:
\[
\frac{408}{600} \approx 0.68 \quad (\text{or } 68\%)
\]
**Step 3: Fill in the relative frequency table.**
\[
\begin{array}{|c|c|c|c|}
\hline
\textbf{Age Group} & \textbf{Prefer Sprinkles (\%)} & \textbf{Prefer Cookie Dough (\%)} & \textbf{Total} \\
\hline
\text{Kids} & 32\% & 68\% & 100\% \\
\hline
\text{Adults} & 32\% & 68\% & 100\% \\
\hline
\end{array}
\]
**Step 4: Determine if there is an association.**
To determine whether there is an association between age group and topping preference, we can examine the relative frequencies for both groups. Since the percentages for preferring sprinkles and cookie dough are the same for kids and adults (32% prefer sprinkles in both groups), there does not appear to be an association based on topping preferences.
**Conclusion:**
- The percentage of kids surveyed that prefer sprinkles is **32%**.
- There is no evidence of an association between age group and topping preference, as the preferences are the same across both groups.