Question

the coach attempts to determine an association between shirt size and hat size. which is most likely true?
an association cannot be determined because 0.48 is similar to 0.52.
an association cannot be determined because the sum of each column is not 1.0.
there is likely an association because 0.8 is not similar to 0.2.
there is likely an association because 0.8 is not similar to ≈0.33.

Explanation:

Step1: Understand association in relative frequency tables

In a relative frequency table, if there is an association between two variables (here, shirt size and hat size), the conditional relative frequencies (e.g., relative frequency of hat size given a shirt size) should be different. If there is no association, the conditional relative frequencies should be similar.

Step2: Analyze the given values

For large - shirted people, the relative frequency of child - sized hats is \(0.2\) and for adult - sized hats is \(0.8\). For the total group, the relative frequency of child - sized hats is \(0.48\) and for adult - sized hats is \(0.52\). Since \(0.8\) (relative frequency of adult - sized hats for large - shirted) is not similar to \(0.52\) (total relative frequency of adult - sized hats), there is an association.

Answer:

There is likely an association because \(0.8\) is not similar to \(0.52\).