Question

the conditional relative frequency table was generated by row using frequency table data comparing the hat size and shirt size of children on a baseball team. normal - probability hat size and shirt size child - sized hat adult - sized hat total medium shirt ≈0.67 ≈0.33 1.0 large shirt 0.2 0.8 1.0 total 0.48 0.52 1.0 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: Analyze conditional relative - frequencies

In a conditional relative - frequency table, if the conditional relative frequencies within rows or columns are very different, it indicates an association.
For large - shirt children, the relative frequency of having an adult - sized hat is 0.8 and the relative frequency of having a child - sized hat is 0.2. For medium - shirt children, the relative frequency of having an adult - sized hat is approximately 0.33 and the relative frequency of having a child - sized hat is approximately 0.67.

Step2: Determine association

The difference between the relative frequencies for different shirt sizes (e.g., 0.8 for large - shirt and adult - sized hat vs 0.33 for medium - shirt and adult - sized hat) shows a non - random pattern. A large difference in conditional relative frequencies implies an association between shirt size and hat size.

Answer:

There is likely an association because 0.8 is not similar to ≈0.33.