Question

the conditional relative frequency table below was generated by column using data comparing gender and a persons favorite meal to cook. which would most likely indicate an association between the categorical variables? the value of a is similar to the value of b. the value of a is similar to the value of e. the value of b is not similar to the value of c. the value of b is not similar to the value of f.

Explanation:

Step1: Understand conditional relative frequency

Conditional relative frequency is used to see the relationship between two categorical variables. If there is an association, the conditional relative frequencies for different categories (in this case, male and female) within the same meal - type (column) should be different.

Step2: Analyze each option

• Option 1: Comparing \(A\) (male - breakfast) and \(B\) (male - lunch) is comparing within the same row (male), not across genders for the same meal type.
• Option 2: Comparing \(A\) (male - breakfast) and \(E\) (female - breakfast) is comparing across genders for the same meal type. But if they are similar, it indicates no association.
• Option 3: Comparing \(B\) (male - lunch) and \(C\) (male - dinner) is comparing within the same row (male), not across genders for the same meal type.
• Option 4: \(B\) is the conditional relative frequency of males who prefer lunch and \(F\) is the conditional relative frequency of females who prefer lunch. If \(B

eq F\), it means that the proportion of males who prefer lunch is different from the proportion of females who prefer lunch. This difference in conditional relative frequencies (for the same meal - type, lunch) across genders (male and female) indicates an association between gender (categorical variable 1) and favorite meal to cook (categorical variable 2).

Answer:

The value of \(B\) is not similar to the value of \(F\).