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 within categories are very different, there is likely an association.

Step2: Analyze the given table

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

Step3: Evaluate the options

Options A and B are incorrect because they give wrong reasons for non - association. Option C compares values within the same row for large - shirt children, but a better comparison is between different shirt - size categories for the same hat - size category. Option D is correct as the difference between the relative frequency of adult - sized hats for large - shirt (0.8) and medium - shirt (≈0.33) children indicates a likely association.

Answer:

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