Purchases More than 2 Pairs per Year

Question

Purchases 2 Pairs or Less per Year

Total
Runs More than 5 Miles per Week

42 28 70
Runs Less than 5 Miles per Week

15 32 47
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. Create a conditional relative frequency table of the data. Use your table to support your reasoning. Explain your reasoning in 3 simple sentences.

Answer 1

To analyze the association between the number of miles run per week and the number of pairs of running shoes purchased, we can create a conditional relative frequency table based on the given data.

Original Data:

• Runs More than 5 Miles per Week:
  • Purchases More than 2 Pairs: 42
  • Purchases 2 Pairs or Less: 28
  • Total: 70
• Runs Less than 5 Miles per Week:
  • Purchases More than 2 Pairs: 15
  • Purchases 2 Pairs or Less: 32
  • Total: 47

Conditional Relative Frequency Table:

• For runners who run more than 5 miles per week:

  • More than 2 pairs: \( \frac{42}{70} = 0.60\) (60%)
  • 2 pairs or less: \( \frac{28}{70} = 0.40\) (40%)

• For runners who run less than 5 miles per week:

  • More than 2 pairs: \( \frac{15}{47} \approx 0.32\) (32%)
  • 2 pairs or less: \( \frac{32}{47} \approx 0.68\) (68%)

Summary Conditional Relative Frequency Table: | | More than 2 Pairs | 2 Pairs or Less | |-----------------------|--------------------|------------------| | More than 5 Miles | 60% | 40% | | Less than 5 Miles | 32% | 68% |

Reasoning: The conditional relative frequency table indicates that runners who run more than 5 miles per week are more likely to purchase more than 2 pairs of shoes (60%) compared to those who run less than 5 miles (32%). This suggests a positive association between running more miles and purchasing more running shoes. Therefore, it can be inferred that runners who engage in more extensive weekly running are likely to buy more pairs of shoes annually.