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 250 408

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  250 408

BlackTom AI · Accepted Answer

We start by restating the given contingency table in our own words to keep track of what is known and what is unknown.
- Attitude columns: Favour, Neutral, Oppose, TOTAL.
- Job classifications (rows): Casual, Part Time, Full Time, TOTAL.
The provided entries are:
Casual row: Favour = 22, Neutral = W, Oppose = V, TOTAL = 121.
Part Time row: Favour = X, Neutral = 12, Oppose = 49, TOTAL = 78.
Full Time row: Favour = 57, Neutral = 38, Oppose = T, TOTAL = Y.
TOTAL row: Favour TOTAL = Z, Neutral TOTAL = U, Oppose TOTAL = 250, TOTAL TOTAL = 408.
Other totals given at the end help connect rows and columns.

1) Solve for X from the Part Time row using its TOTAL.
- In Part Time: X + 12 + 49 = 78.
- Therefore X = 78 - 61 = 17.

2) Use column totals to find Z and U, starting with the Favour column total.
- Favour column total Z = Casual Favour 22 + Part Time Favour X (17) + Full Time Favour 57.
- So Z = 22 + 17 + 57 = 96.
- Neutral column total U involves Casual Neutral W plus Part Time Neutral 12 plus Full Time Neutral 38.
- Thus U = W + 12 + 38 = W + 50.

3) Use the Oppose column total to relate V and T.
- Oppose column total is 250, consisting of Casual V + Part Time Oppose 49 + Full Time Oppose T.
- So V + T + 49 = 250, hence V + T = 201.

4) Use the TOTAL row to connect Full Time totals and the grand total.
- Full Time TOTAL equals Favour 57 + Neutral 38 + Oppose T = 95 + T.
- The grand total across all rows should be 408, so 121 (Casual total) + 78 (Part Time total) + (95 + T) (Full Time total) = 408.
- Compute: 121 + 78 + 95 + T = 408 → 294 + T = 408 → T = 114.

5) Back-substitute to find V.
- From V + T = 201 and T = 114, we get V = 201 - 114 = 87.

6) Finally, determine W using the Casual row total.
- Casual TOTAL is 121, and Casual entries are Favour 22, Neutral W, Oppose V, so 22 + W + 87 = 121.
- Therefore W = 121 - 22 - 87 = 12.

7) Sanity check (optional but good practice).
- Check Part Time total: X = 17, Neutral 12, Oppose 49 → 17 + 12 + 49 = 78, which matches the given Part Time TOTAL.
- Check Favour column total: 22 (Casual) + 17 (Part Time) + 57 (Full Time) = 96, so Z = 96.
- Check Neutral total: W + 12 + 38 = 12 + 12 + 38 = 62, so U = 62; later U = W + 50 gives 12 + 50 = 62, consistent.
- Check Oppose total:  V + 49 + 114 = 87 + 49 + 114 = 250, matches the given total.
- Check grand total: 121 + 78 + (57 + 38 + 114) = 121 + 78 + 209 = 408, matches the grand total.

Through these steps, we have deduced the missing values consistently and verified internal arithmetic across rows and columns.

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 250 408

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