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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.

To determine the potential correlation between a runner's weekly mileage and their yearly running shoe purchases, a conditional relative frequency table can be constructed. Initially, the totals of runners purchasing over 2 pairs (70) and those purchasing 2 pairs or fewer (47) are calculated, as well as the totals of runners running over 5 miles weekly (57) and those running under 5 miles weekly (60). Subsequently, each category's frequency is divided by its respective total, creating the conditional relative frequency table. By examining this data, any relationship between the variables can be identified. Through this analysis, it can be determined if the number of miles run per week is associated with the number of pairs of running shoes purchased annually.