Question

a conditional relative frequency table is generated by column from a set of data. the conditional relative frequencies of the two categorical variables are then compared.
if the relative frequencies being compared are 0.21 and 0.79, which conclusion is most likely supported by the data?
○ an association cannot be determined between the categorical variables because the relative frequencies are not similar in value.
○ there is likely an association between the categorical variables because the relative frequencies are not similar in value.
○ an association cannot be determined between the categorical variables because the sum of the relative frequencies is 1.0.
○ there is likely an association between the categorical variables because the sum of the relative frequencies is 1.0.

Explanation:

1. Recall the concept of conditional relative frequency and association between categorical variables: When comparing conditional relative frequencies (from a column - generated table), if the frequencies are not similar, it suggests an association. The sum of relative frequencies in a category being 1.0 is a given (since they are relative frequencies for a category) and doesn't affect the determination of association.
2. Analyze each option:

• Option 1: Incorrect. Different relative frequencies (not similar) can indicate an association, not that it can't be determined.
• Option 2: Correct. When conditional relative frequencies (from a column - based table) are not similar, it is likely that there is an association between the categorical variables.
• Option 3: Incorrect. The sum of relative frequencies being 1.0 is a property of relative frequencies (they sum to 1 for a given group) and has nothing to do with determining association.
• Option 4: Incorrect. The sum of relative frequencies being 1.0 is a basic property and does not imply an association. The association is determined by the difference in relative frequencies.

Answer:

There is likely an association between the categorical variables because the relative frequencies are not similar in value.