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

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 analyze the association between weekly running miles and annual shoe purchases, we can create a conditional relative frequency table based on the provided data. First, we find the total number of runners: 42 + 28 + 15 + 32 = 117. Next, we calculate the relative frequencies based on each category.

Conditional Relative Frequency Table:

| | Purchase > 2 pairs | Purchase < 2 pairs | Row Total | |---------------------|---------------------|---------------------|-----------| | Run > 5 miles/week | 42 / 117 = 0.36 | 28 / 117 = 0.24 | 70 / 117 = 0.60 | | Run < 5 miles/week | 15 / 117 = 0.13 | 32 / 117 = 0.27 | 47 / 117 = 0.40 | | Column Total | 57 / 117 = 0.49 | 60 / 117 = 0.51 | 117 |

This table indicates that a higher proportion of runners who run more than 5 miles a week (36%) purchase more than 2 pairs of shoes compared to those who run less than 5 miles a week (13%). Conversely, a greater percentage of runners who run less than 5 miles a week (27%) purchase less than 2 pairs of shoes compared to those who run more than 5 miles (24%). Thus, there appears to be an association between running distance and shoe purchases, suggesting that more dedicated runners tend to buy more shoes.