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 3sentences. Please make the sentence short, simple, and to the point.

Answer 1

First, we calculate the total number of participants, which is 42 + 28 + 15 + 32 = 117. Next, we create a conditional relative frequency table based on the number of pairs purchased, using the total in each category for the calculations.

Conditional Relative Frequency Table:

| Purchase Pairs | More than 2 pairs | Less than 2 pairs | Total | |------------------|-------------------|--------------------|-------| | Run more than 5 miles | 42/57 ≈ 0.74 | 28/57 ≈ 0.26 | 57 | | Run less than 5 miles | 15/47 ≈ 0.32 | 32/47 ≈ 0.68 | 47 | | Total | 57 | 47 | 117 |

From the table, 74% of participants who run more than 5 miles a week purchase more than 2 pairs of shoes, compared to only 32% of those who run less than 5 miles. This suggests a strong association between running more miles and purchasing more shoes. Therefore, as running distance increases, so does the likelihood of purchasing more running shoes.