A running shoe company collecting data on long distance runners the company's research analyst as 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 and individual runs per week and how many pairs of running shoes they purchase per year create a condition relative frequency table of the data use your table to support your reasoning explain your reasoning and three sentences

Question

A running shoe company collecting data on long distance runners the company's research analyst as 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 and individual runs per week and how many pairs of running shoes they purchase per year create a condition relative frequency table of the data use your table to support your reasoning explain your reasoning and three sentences 
Purchases more than two pairs per year purchase the 42 purchases two pairs or less per year 28 total 70 runs more than 5 mph 42 and 28 which equals 70 runs less than 5 mi per week purchase is more than two pairs per year 15 runs less than five miles per week perches is two pairs or less per year 32 total 47

GPT-4o mini · Answer

To determine if there is an association between the number of miles runners run per week and the number of pairs of running shoes they purchase per year, we can create a relative frequency table and analyze the data.

Relative Frequency Table:

| | Purchases > 2 Pairs | Purchases ≤ 2 Pairs | Total | |---------------------|----------------------|----------------------|-------| | Runs > 5 miles/week | 42 | 28 | 70 | | Runs ≤ 5 miles/week | 15 | 32 | 47 | | Total | 57 | 60 | 117 |

Now, we can compute the relative frequencies for each category:

Relative frequency of runners purchasing more than 2 pairs of shoes and running more than 5 miles/week:
\( \frac{42}{117} \approx 0.359 \) (or 35.9%)
Relative frequency of runners purchasing ≤ 2 pairs of shoes and running more than 5 miles/week:
\( \frac{28}{117} \approx 0.239 \) (or 23.9%)
Relative frequency of runners purchasing more than 2 pairs of shoes and running ≤ 5 miles/week:
\( \frac{15}{117} \approx 0.128 \) (or 12.8%)
Relative frequency of runners purchasing ≤ 2 pairs of shoes and running ≤ 5 miles/week:
\( \frac{32}{117} \approx 0.273 \) (or 27.3%)

Conclusion: Based on the relative frequencies, a larger proportion of runners who run more than 5 miles per week purchase more than 2 pairs of shoes (35.9%) compared to those who run 5 miles or less and purchase more than 2 pairs (12.8%). This suggests a positive association between running more miles per week and the likelihood of purchasing more running shoes. Thus, it can be reasoned that the greater the mileage run per week, the more pairs of shoes are purchased by that individual.