Question
A running shoe company is collecting data on long-distance runners. The company's research analyst asked runners how many pairs of running shoes they purchase each year and how many miles they run each week, on average. The results are summarized in the table.
runs more than 5 miles per week: purchases more than 2 pairs per year:42 purchases 2 pairs or less per year: 28 runs less than 5 miles per week: purchases more than 2 pairs per year: 15 purchases 2 pairs or less per year: 32
Drag and drop the correct percentage to fill out the conditional relative frequency table of the data.
(4 points)
Drop target 1
Drop target 2
Drop target 3
Drop target 4
32% 40% 60% 68%
Question 2
Based on your conditional relative frequency table, is there an association between the number of miles an individual runs per week and how many pairs of running shoes they purchase a year?
You MUST provide 1 detail from your table that supports your decision. in simple words
(2 points)
runs more than 5 miles per week: purchases more than 2 pairs per year:42 purchases 2 pairs or less per year: 28 runs less than 5 miles per week: purchases more than 2 pairs per year: 15 purchases 2 pairs or less per year: 32
Drag and drop the correct percentage to fill out the conditional relative frequency table of the data.
(4 points)
Drop target 1
Drop target 2
Drop target 3
Drop target 4
32% 40% 60% 68%
Question 2
Based on your conditional relative frequency table, is there an association between the number of miles an individual runs per week and how many pairs of running shoes they purchase a year?
You MUST provide 1 detail from your table that supports your decision. in simple words
(2 points)
Answers
GPT-4o mini
To fill out the conditional relative frequency table based on the data provided, we first calculate the total number of respondents in each category.
1. **Total running more than 5 miles per week**: 42 (purchases more than 2 pairs) + 28 (purchases 2 pairs or less) = 70
2. **Total running less than 5 miles per week**: 15 (purchases more than 2 pairs) + 32 (purchases 2 pairs or less) = 47
Next, we can calculate the conditional relative frequencies:
### For runners running more than 5 miles per week:
- **Purchases more than 2 pairs**:
\[
\frac{42}{70} \times 100 = 60\%
\]
- **Purchases 2 pairs or less**:
\[
\frac{28}{70} \times 100 = 40\%
\]
### For runners running less than 5 miles per week:
- **Purchases more than 2 pairs**:
\[
\frac{15}{47} \times 100 \approx 31.91\% \text{ (which can be rounded to 32\% for the table)}
\]
- **Purchases 2 pairs or less**:
\[
\frac{32}{47} \times 100 \approx 68.09\% \text{ (which can be rounded to 68\% for the table)}
\]
Now we fill in the conditional relative frequency table as follows:
- Runners running more than 5 miles per week:
- Purchases more than 2 pairs per year: 60%
- Purchases 2 pairs or less per year: 40%
- Runners running less than 5 miles per week:
- Purchases more than 2 pairs per year: 32%
- Purchases 2 pairs or less per year: 68%
### Final condition relative frequency table:
- **Drop Target 1**: 60%
- **Drop Target 2**: 40%
- **Drop Target 3**: 32%
- **Drop Target 4**: 68%
---
### Question 2
Based on the conditional relative frequency table, there **is** an association between the number of miles an individual runs per week and how many pairs of running shoes they purchase per year.
**Support Detail**: For runners who run more than 5 miles per week, 60% purchase more than 2 pairs of shoes each year, while only 32% of those who run less than 5 miles per week do the same. This suggests that as mileage increases, the likelihood of purchasing more shoes also increases, indicating a potential association.
1. **Total running more than 5 miles per week**: 42 (purchases more than 2 pairs) + 28 (purchases 2 pairs or less) = 70
2. **Total running less than 5 miles per week**: 15 (purchases more than 2 pairs) + 32 (purchases 2 pairs or less) = 47
Next, we can calculate the conditional relative frequencies:
### For runners running more than 5 miles per week:
- **Purchases more than 2 pairs**:
\[
\frac{42}{70} \times 100 = 60\%
\]
- **Purchases 2 pairs or less**:
\[
\frac{28}{70} \times 100 = 40\%
\]
### For runners running less than 5 miles per week:
- **Purchases more than 2 pairs**:
\[
\frac{15}{47} \times 100 \approx 31.91\% \text{ (which can be rounded to 32\% for the table)}
\]
- **Purchases 2 pairs or less**:
\[
\frac{32}{47} \times 100 \approx 68.09\% \text{ (which can be rounded to 68\% for the table)}
\]
Now we fill in the conditional relative frequency table as follows:
- Runners running more than 5 miles per week:
- Purchases more than 2 pairs per year: 60%
- Purchases 2 pairs or less per year: 40%
- Runners running less than 5 miles per week:
- Purchases more than 2 pairs per year: 32%
- Purchases 2 pairs or less per year: 68%
### Final condition relative frequency table:
- **Drop Target 1**: 60%
- **Drop Target 2**: 40%
- **Drop Target 3**: 32%
- **Drop Target 4**: 68%
---
### Question 2
Based on the conditional relative frequency table, there **is** an association between the number of miles an individual runs per week and how many pairs of running shoes they purchase per year.
**Support Detail**: For runners who run more than 5 miles per week, 60% purchase more than 2 pairs of shoes each year, while only 32% of those who run less than 5 miles per week do the same. This suggests that as mileage increases, the likelihood of purchasing more shoes also increases, indicating a potential association.