People that run more than 5 miles a week & purchase more than 2 pairs of a year: 42

Question

People that run more than 5 miles a week & purchase less than 2 pairs a year: 28
People that run less than 5 miles a week & purchase more than 2 pairs a year: 15
People that run less than 5 miles a week & purchase less than 2 pairs a year: 32
People that run more than 5 miles a week total: 70
People that run less than 5 miles a week total: 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 sentences. Please make the sentence short, simple, and to the point, nothing complicated.

Answer 1

To create a conditional relative frequency table, we first need to calculate the total number of people in each running category. The total for those who run more than 5 miles a week is 70, and for those who run less than 5 miles a week, it is 47. Each category is as follows:

1. People running more than 5 miles and purchasing more than 2 pairs: 42
2. People running more than 5 miles and purchasing less than 2 pairs: 28
3. People running less than 5 miles and purchasing more than 2 pairs: 15
4. People running less than 5 miles and purchasing less than 2 pairs: 32

Conditional Relative Frequency Table:

| Miles/ Shoes | More than 2 pairs | Less than 2 pairs | Total | |-------------------------------|-------------------|-------------------|-------| | More than 5 miles | 42 (60%) | 28 (40%) | 70 | | Less than 5 miles | 15 (32%) | 32 (68%) | 47 |

Totals:

• More than 2 pairs: 57 (42 + 15)
• Less than 2 pairs: 60 (28 + 32)

From this table, the frequency of runners purchasing more than 2 pairs of shoes is higher among those running more than 5 miles per week (60%). This indicates that there is a positive association between running more miles and purchasing more running shoes. Therefore, as running distance increases, so does the likelihood of buying additional pairs of shoes.