To determine if there is an association between the number of miles an individual runs per week and the number of pairs of running shoes they purchase per year, we first need to create a conditional relative frequency table from the data provided. This table will show the proportion of runners within each mileage category that purchase a certain number of pairs of shoes.
Suppose the initial table of raw data might look like this (just as a hypothetical example):
| Miles per Week | 1 Pair | 2 Pairs | 3 Pairs | |----------------|--------|---------|---------| | 0 - 10 | 10 | 5 | 1 | | 11 - 20 | 4 | 10 | 6 | | 21 - 30 | 2 | 8 | 8 | | 31 - 40 | 1 | 2 | 9 |
Next, we will calculate the row totals and the relative frequencies. The conditional relative frequency for each cell will be the count in that cell divided by the total count of that row.
After completing those calculations, the conditional relative frequency table might look like this:
| Miles per Week | 1 Pair | 2 Pairs | 3 Pairs | |----------------|--------|---------|---------| | 0 - 10 | 0.62 | 0.31 | 0.08 | | 11 - 20 | 0.14 | 0.35 | 0.21 | | 21 - 30 | 0.08 | 0.32 | 0.32 | | 31 - 40 | 0.04 | 0.08 | 0.36 |
Now, to interpret this table:
- For runners who log between 0-10 miles per week, a significant majority (62%) purchase only one pair of shoes.
- As the mileage categories increase, the relative frequency of purchasing three pairs also increases, particularly in the 31-40 miles category where 36% opt for three pairs.
- This pattern suggests a positive association—those who run more miles seem to buy more pairs of shoes annually, supporting the idea that greater mileage correlates with higher shoe consumption.
Thus, based on this table and the observed trends, we can conclude that there is an association between the number of miles run per week and the number of running shoes purchased each year. The analysis shows that runners who log more miles tend to buy more pairs of shoes, indicating that mileage may influence shoe purchasing habits.