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.
(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.
(2 points)
Answers
GPT-4o mini
To fill out the conditional relative frequency table, we need to calculate the percentages based on the total number of runners in each category (runs more than 5 miles and runs less than 5 miles).
First, let's organize the data:
1. For runners who run more than 5 miles per week:
- Purchases more than 2 pairs per year: 42
- Purchases 2 pairs or less per year: 28
- **Total:** 42 + 28 = 70
2. For runners who run less than 5 miles per week:
- Purchases more than 2 pairs per year: 15
- Purchases 2 pairs or less per year: 32
- **Total:** 15 + 32 = 47
Now, we will calculate the conditional relative frequencies:
**For runners who run more than 5 miles per week:**
1. Purchases more than 2 pairs per year: \( \frac{42}{70} \times 100 = 60\% \)
2. Purchases 2 pairs or less per year: \( \frac{28}{70} \times 100 = 40\% \)
**For runners who run less than 5 miles per week:**
1. Purchases more than 2 pairs per year: \( \frac{15}{47} \times 100 \approx 31.91\% \) (rounded to 32%)
2. Purchases 2 pairs or less per year: \( \frac{32}{47} \times 100 \approx 68.09\% \) (rounded to 68%)
Putting this into a conditional relative frequency table:
| Miles per week | More than 2 pairs | 2 pairs or less |
|----------------------|--------------------|------------------|
| More than 5 | 60% | 40% |
| Less than 5 | 32% | 68% |
### Filled-in Conditional Relative Frequency Table:
1. Drop target 1: **60%**
2. Drop target 2: **40%**
3. Drop target 3: **32%**
4. Drop target 4: **68%**
### Question 2:
Based on the conditional relative frequency table, there appears to be an association between the number of miles an individual runs per week and the number of pairs of running shoes they purchase annually.
**Supporting detail:** For runners who run more than 5 miles per week, 60% purchase more than 2 pairs of shoes per year, while only 32% of those who run less than 5 miles per week purchase more than 2 pairs. This shows that runners who run more tend to buy more shoes, indicating a potential association.
First, let's organize the data:
1. For runners who run more than 5 miles per week:
- Purchases more than 2 pairs per year: 42
- Purchases 2 pairs or less per year: 28
- **Total:** 42 + 28 = 70
2. For runners who run less than 5 miles per week:
- Purchases more than 2 pairs per year: 15
- Purchases 2 pairs or less per year: 32
- **Total:** 15 + 32 = 47
Now, we will calculate the conditional relative frequencies:
**For runners who run more than 5 miles per week:**
1. Purchases more than 2 pairs per year: \( \frac{42}{70} \times 100 = 60\% \)
2. Purchases 2 pairs or less per year: \( \frac{28}{70} \times 100 = 40\% \)
**For runners who run less than 5 miles per week:**
1. Purchases more than 2 pairs per year: \( \frac{15}{47} \times 100 \approx 31.91\% \) (rounded to 32%)
2. Purchases 2 pairs or less per year: \( \frac{32}{47} \times 100 \approx 68.09\% \) (rounded to 68%)
Putting this into a conditional relative frequency table:
| Miles per week | More than 2 pairs | 2 pairs or less |
|----------------------|--------------------|------------------|
| More than 5 | 60% | 40% |
| Less than 5 | 32% | 68% |
### Filled-in Conditional Relative Frequency Table:
1. Drop target 1: **60%**
2. Drop target 2: **40%**
3. Drop target 3: **32%**
4. Drop target 4: **68%**
### Question 2:
Based on the conditional relative frequency table, there appears to be an association between the number of miles an individual runs per week and the number of pairs of running shoes they purchase annually.
**Supporting detail:** For runners who run more than 5 miles per week, 60% purchase more than 2 pairs of shoes per year, while only 32% of those who run less than 5 miles per week purchase more than 2 pairs. This shows that runners who run more tend to buy more shoes, indicating a potential association.