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.
hat size and shirt size

	child - sized hat	adult - sized hat	total
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: Understand conditional relative - frequency

Conditional relative - frequency helps in determining associations. If the conditional relative frequencies for different categories are very different, there is likely an association.

Step2: Analyze the given table

For children with large shirts, the conditional relative - frequency of having an adult - sized hat is 0.8, and for children with medium shirts, the conditional relative - frequency of having an adult - sized hat is approximately 0.33. These two values are quite different.

Step3: Evaluate the options

The fact that 0.8 is not similar to approximately 0.33 indicates a likely association between shirt size and hat size.

Answer:

There is likely an association because 0.8 is not similar to $\approx0.33$.