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. Determine if 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. Complete the conditional relative frequency table of the data. Then use the drop-down options to complete the conclusion sentences.

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. Determine if 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.  Complete the conditional relative frequency table of the data. Then use the drop-down options to complete the conclusion sentences.

(5 points)
 	Purchases More than 2 Pairs Per Year	Purchases 2 Pairs or Less Per Year	Total
Runs More than 5 Miles Per Week

Runs Less than 5 Miles Per Week

Of the survey respondents who run more than five miles per week, 
% purchase more than two pairs of shoes per year, and 
% purchase two pairs or less.

Of the survey respondents who run less than five miles per week, 
% purchase more than two pairs of shoes per year and 
% purchase two pairs or less.

The frequency table shows 
 between how many shoes are purchased given the number of miles per week a person runs. Therefore, there is 
 between the number of miles a person runs per week and how many pairs of running shoes they purchase per year.

GPT-4o mini · Answer

To complete the task, we first need to outline the collected data and create a conditional relative frequency table based on that data regarding the number of pairs of running shoes purchased per year and the average miles run per week.

However, since the data itself is not provided in your question, I'll provide a general outline of how to approach the completion of the conditional relative frequency table and draw conclusions based on hypothetical numbers.

Fictitious Data Example: Let's assume the following data summarizes the runners surveyed:
- Runs More than 5 Miles Per Week:
  - Purchases More than 2 Pairs Per Year: 30
  - Purchases 2 Pairs or Less Per Year: 20
- Runs Less than 5 Miles Per Week:
  - Purchases More than 2 Pairs Per Year: 10
  - Purchases 2 Pairs or Less Per Year: 40
Now we can fill the total column and calculate the conditional relative frequencies.

Total Row Calculations:

Total for Runs More than 5 Miles Per Week = 30 + 20 = 50
Total for Runs Less than 5 Miles Per Week = 10 + 40 = 50

Total Purchases Column:

Total Purchases More than 2 Pairs = 30 + 10 = 40
Total Purchases 2 Pairs or Less = 20 + 40 = 60

Overall Total:
```
Overall Total = 50 + 50 = 100
```
Conditional Relative Frequencies:
- For those who run more than 5 miles per week:
  - Purchases More than 2 Pairs Per Year: \( \frac{30}{50} \times 100 = 60% \)
  - Purchases 2 Pairs or Less Per Year: \( \frac{20}{50} \times 100 = 40% \)
- For those who run less than 5 miles per week:
  - Purchases More than 2 Pairs Per Year: \( \frac{10}{50} \times 100 = 20% \)
  - Purchases 2 Pairs or Less Per Year: \( \frac{40}{50} \times 100 = 80% \)

Conditional Relative Frequency Table:

              | Purchases More than 2 Pairs | Purchases 2 Pairs or Less | Total
-----------------------------------------------------------------------
Runs More than 5 Miles Per Week  |          60%              |          40%            |  100%
-----------------------------------------------------------------------
Runs Less than 5 Miles Per Week   |          20%              |          80%            |  100%

Conclusions: You can now fill in the text based on these calculations:

Of the survey respondents who run more than five miles per week, 60% purchase more than two pairs of shoes per year, and 40% purchase two pairs or less.

Of the survey respondents who run less than five miles per week, 20% purchase more than two pairs of shoes per year and 80% purchase two pairs or less.

The frequency table shows an association between how many shoes are purchased given the number of miles per week a person runs. Therefore, there is a positive correlation between the number of miles a person runs per week and how many pairs of running shoes they purchase per year.

Feel free to adjust your conclusions according to the actual data you have!