For the following partially completed contingency table, find the missing value for W. Attitude Job Classification Favour Neutral Oppose TOTAL Casual 22 W V 121 Part Time X 12 49 78 Full Time 57 38 T Y TOTAL Z U 250 426

Question

For the following partially completed contingency table, find the missing value for W. Attitude Job Classification Favour Neutral Oppose TOTAL Casual 22 W  V  121 Part Time X  12 49 78 Full Time 57 38 T  Y  TOTAL Z  U  250 426

BlackTom AI · Accepted Answer

We are given a partially completed contingency table with Attitude as columns (Favour, Neutral, Oppose, TOTAL) and Job Classification as rows (Casual, Part Time, Full Time), and some missing values represented by W, V, X, T, Y, Z, U. The rightmost column provides row totals, and the bottom row provides column totals.

First, determine the value of Y (the TOTAL for Full Time):
- Casual row total is 121, and Casual row entries are 22 (Favour), W (Neutral), V (Oppose).
- Part Time row total is 78, with X (Favour), 12 (Neutral), 49 (Oppose).
- Full Time row total is Y, with 57 (Favour), 38 (Neutral), T (Oppose).
So 22 + W + V = 121 -> W + V = 99. Also 57 + 38 + T = Y -> 95 + T = Y.
The bottom-right entry Y (the TOTAL of all three rows) plus the other row totals should equal the overall total 426. The sum of the first two row totals is 121 + 78 = 199, so Y = 426 − 199 = 227.
Thus T = Y − 95 = 227 − 95 = 132.

Next, use the column total for Oppose, which is 250 (the total across all rows for the Oppose column):
- Oppose entries are V (Casual), 49 (Part Time), T (Full Time).
So V + 49 + 132 = 250 -> V = 250 − 181 = 69.
Then W = (W + V) − V = 99 − 69 = 30.

Now compute the remaining missing column totals:
- Z is the total Favour across all rows: Z = 22 (Casual) + X (Part Time) + 57 (Full Time).
From Part Time, X + 12 + 49 = 78 -> X = 17. Therefore Z = 22 + 17 + 57 = 96.
- U is the total Neutral across all rows: U = W (Casual) + 12 (Part Time) + 38 (Full Time) = 30 + 12 + 38 = 80.

Summary of findings for the missing value W:
- W equals 30, not 38. The provided value of 38 would violate the row total constraint for the Casual row (22 + 30 + 69 = 121) and would disrupt the overall column totals (e.g., Oppose total would be 69 + 49 + 132 = 250 still, but the Neutral total and the W value would no longer align with the given Neutral column total U = 80). The correct internal consistency checks lead to W = 30.

Additional consistency checks:
- Casual row: 22 (Favour) + 30 (Neutral) + 69 (Oppose) = 121, which matches the row total 121.
- Part Time: X = 17, plus 12 and 49 gives 78, matching the row total.
- Full Time: 57 + 38 + 132 = 227, matching Y.
- Column Totals: Favour total Z = 22 + 17 + 57 = 96; Neutral total U = 30 + 12 + 38 = 80; Oppose total 69 + 49 + 132 = 250; Overall total 96 + 80 + 250 = 426, which matches the bottom-right total.

For the following partially completed contingency table, find the missing value for W. Attitude Job Classification Favour Neutral Oppose TOTAL Casual 22 W V 121 Part Time X 12 49 78 Full Time 57 38 T Y TOTAL Z U 250 426

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