which value for y in the table would be least likely to indicate an association between the…

Explanation:

Step1: Recall independence concept

If two - way table variables are independent, the row - column products should follow a certain pattern. In a two - way table, if the variables are independent, the proportion of values in each cell should be consistent with the marginal proportions. For independence, the value of (Y) should make the distribution of values in the (A) and (B) columns similar across the (C), (D), and (E) rows. When the variables are independent, the relative frequencies in each row for the two columns should be similar. The total of column (B) is (1.0), and the values in column (B) for rows (C), (D), and (E) are (0.25), (0.68), and (0.07) respectively. The total of column (A) is also (1.0). If the variables are independent, the ratio of values in column (A) to column (B) for each row should be approximately the same. The closer the value of (Y) is to the proportion of the other non - (Y) values in column (A) relative to the non - (0.68) values in column (B), the less likely there is an association. The sum of non - (Y) values in column (A) is (X + Z=1 - Y), and the sum of non - (0.68) values in column (B) is (0.25 + 0.07=0.32). If the variables are independent, we expect the ratios to be similar. A value of (Y = 0.24) would make the distribution of values in the two columns more evenly distributed across the rows, suggesting less of an association.

Step2: Analyze other options

• If (Y = 0.06), the difference in the distribution of values between the two columns across rows becomes more pronounced, indicating a possible association.
• If (Y = 0.69), it is very different from the proportion of values in the other rows for column (B), suggesting an association.
• If (Y = 1.0), then all of the values in row (D) for column (A) are accounted for, and it creates a very non - uniform distribution across the rows, indicating a strong association.

Answer:

B. (0.24)