Use the table to answer the question.

 
Purchases More than 2 Pairs per Year

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 3–5 sentences.

To determine if there is an association between the number of miles a runner runs per week and the number of pairs of running shoes they purchase per year, we can create a conditional relative frequency table. First, calculate the total number of runners who purchase more than 2 pairs per year (42 + 28 = 70) and the total number of runners who purchase 2 pairs or less per year (15 + 32 = 47). Then, calculate the total number of runners who run more than 5 miles per week (42 + 15 = 57) and the total number of runners who run less than 5 miles per week (28 + 32 = 60). Finally, create the conditional relative frequency table by dividing the frequency of each category by its corresponding total. By analyzing the data in the conditional relative frequency table, we can determine if there is an association between the two variables.