Question

which value for y in the table would be least likely to indicate an association between the variables? 0.06 0.24 0.69 1.0

Explanation:

Step1: Recall the concept of independence

If two variables are independent, the joint - probabilities follow the rule that the probability of the intersection of two events is the product of their marginal probabilities. In a two - way table, when there is no association (i.e., variables are independent), the cell frequencies are distributed in a way that the row and column totals are proportionally related. For a two - way table with rows and columns, if there is no association, the values in the cells should be such that the distribution of one variable does not depend on the other.

Step2: Analyze the given table

We know that the sum of probabilities in each row and each column must equal 1. The column totals for A and B are both 1.0. For no association, the values in the cells should be distributed in a way that the proportion of values in each row is the same across columns. When \(Y = 0.24\), the distribution of values in rows C, D, and E across columns A and B seems more evenly distributed compared to other values.
If \(Y = 0.06\), the difference between the values in column B for rows D and C is large. If \(Y=0.69\), it makes the proportion in row D very different from the other rows in terms of the split between A and B. If \(Y = 1.0\), it means all of row D is in category A, which is a very extreme non - even distribution.

Answer:

0.24