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 independence concept

If two variables are independent, the joint - probabilities follow the rule \(P(A\cap B)=P(A)\times P(B)\). In a two - way frequency table, when there is no association between the variables, the relative frequencies in each row and column should be consistent with what we would expect if the variables were independent.

We know that the sum of the values in the 'B' column is 1.0 (\(0.25 + 0.68+0.07 = 1.0\)). And the sum of the values in the 'A' column is 1.0.

If there is no association, the proportion of values in each cell should be such that the row and column totals are consistent with random distribution.

The value of \(Y\) should be such that it does not create a non - random pattern.

We note that if \(Y = 0.24\), the distribution of values in the table would be more in line with what we would expect if the variables were independent.

If \(Y = 0.06\), it creates a more skewed pattern in the table compared to \(Y = 0.24\). If \(Y=0.69\), it also creates a non - random pattern as it is very close to the value in the same row for the 'B' column (\(0.68\)) and may suggest a non - independent relationship. If \(Y = 1.0\), it is an extreme and non - realistic value for a cell in a two - way frequency table where the column and row totals are 1.0 and would clearly indicate a non - random (associated) relationship.

Step2: Select the least - likely value for association

The value of \(Y\) that is least likely to indicate an association between the variables is \(0.24\).

Answer:

0.24