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 start by identifying what each cell represents and what totals are given in the partially completed contingency table.

- The table has Attitude as rows (Favour, Neutral, Oppose, TOTAL) and Job Classification as columns (Casual, Part Time, Full Time, TOTAL).
- For the Casual row: Favour = 22, Neutral = W, Oppose = V, and the row TOTAL is 121. So W + V + 22 = 121, which gives W + V = 99.

- For the Part Time row: Favour = X, Neutral = 12, Oppose = 49, and the row TOTAL is 78. Thus X + 12 + 49 = 78, giving X = 78 − 61 = 17.

- For the Full Time row: Favour = 57, Neutral = 38, Oppose = T, and the row TOTAL is Y. Therefore 57 + 38 + T = Y, which means T = Y − 95.

- The bottom row provides the TOTALs for each column and the grand total: Favour column TOTAL = Z, Neutral column TOTAL = U, Oppose column TOTAL = 250, and overall TOTAL = 426.

Next, use the overall total to determine the Full Time row total Y.
- Sum of the known row totals: Casual (121) + Part Time (78) + Full Time (Y) = Overall TOTAL (426).
- So 121 + 78 + Y = 426 → 199 + Y = 426 → Y = 426 − 199 = 227.

With Y known, compute T (Oppose in Full Time):
- In Full Time, 57 + 38 + T = 227 → 95 + T = 227 → T = 132.

Now examine the Oppose column total, which is given as 250:
- Oppose total = V (Casual) + 49 (Part Time) + 132 (Full Time) = 250.
- Therefore V = 250 − 181 = 69.

Return to the Casual row to find W using W + V = 99: 
- W = 99 − V = 99 − 69 = 30.

With W found, you could also check the Neutral column total: Neutral column U would be W + 12 + 38 = 30 + 12 + 38 = 80, and the Favour column total Z would be 22 + 17 + 57 = 96, which together with the other column totals sums to the grand total 426 as a consistency check.

Summary of the key steps:
- Use row totals to find Y (Full Time total) from 121 + 78 + Y = 426 → Y = 227.
- Use Y to find T (Oppose in Full Time) from 57 + 38 + T = 227 → T = 132.
- Use Oppose column total 250 to solve for V from V + 49 + 132 = 250 → V = 69.
- Use Casual row total 121 to find W from W + V + 22 = 121 → W = 99 − 69 = 30.

Thus, the missing value W is 30.

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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