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Answer :
To classify the results for each category as either consistent or inconsistent with the model, let's follow a step-by-step process using the grocery store's data.
### Given Data:
- Model Percentage for Soccer Balls: 58%
- Week 1: 85 soccer balls, 30 baseball bats, 31 tennis rackets
- Week 2: 110 soccer balls, 22 baseball bats, 23 tennis rackets
- Week 3: 64 soccer balls, 21 baseball bats, 23 tennis rackets
### Step-by-Step Solution:
#### 1. Calculate Total Purchases Each Week:
- Week 1: \( 85 + 30 + 31 = 146 \)
- Week 2: \( 110 + 22 + 23 = 155 \)
- Week 3: \( 64 + 21 + 23 = 108 \)
#### 2. Calculate Expected Soccer Ball Purchases According to the Model:
- Expected Week 1: \( 0.58 \times 146 = 84.68 \)
- Expected Week 2: \( 0.58 \times 155 = 89.9 \)
- Expected Week 3: \( 0.58 \times 108 = 62.64 \)
#### 3. Calculate Total Purchases for All Three Weeks:
- Total All Weeks: \( 146 + 155 + 108 = 409 \)
- Expected All Weeks: \( 0.58 \times 409 = 237.22 \)
#### 4. Determine Consistency:
For each week and the total, we check if the actual soccer ball purchases are within 5% of the model prediction.
- Allowed Deviation:
- For Week 1: \( 0.05 \times 146 = 7.3 \)
- For Week 2: \( 0.05 \times 155 = 7.75 \)
- For Week 3: \( 0.05 \times 108 = 5.4 \)
- For Total 3 weeks: \( 0.05 \times 409 = 20.45 \)
#### 5. Consistency Check:
- Week 1:
- Actual: 85
- Expected: 84.68
- Allowed Deviation: 7.3
- \( |85 - 84.68| = 0.32 \) which is \(\leq\) 7.3 (Consistent)
- Week 2:
- Actual: 110
- Expected: 89.9
- Allowed Deviation: 7.75
- \( |110 - 89.9| = 20.1 \) which is \(>\) 7.75 (Inconsistent)
- Week 3:
- Actual: 64
- Expected: 62.64
- Allowed Deviation: 5.4
- \( |64 - 62.64| = 1.36 \) which is \(\leq\) 5.4 (Consistent)
- Total All Weeks:
- Actual: \( 85 + 110 + 64 = 259 \)
- Expected: 237.22
- Allowed Deviation: 20.45
- \( |259 - 237.22| = 21.78 \) which is \(>\) 20.45 (Inconsistent)
### Final Classification:
| Consistent with Model | Inconsistent with Model |
|------------------------|----------------------------------|
| Week 1 results | Week 2 results |
| Week 3 results | Total of all 3 weeks' results |
You can now drag the classifications to the respective cells in the table based on the computed consistencies.
### Given Data:
- Model Percentage for Soccer Balls: 58%
- Week 1: 85 soccer balls, 30 baseball bats, 31 tennis rackets
- Week 2: 110 soccer balls, 22 baseball bats, 23 tennis rackets
- Week 3: 64 soccer balls, 21 baseball bats, 23 tennis rackets
### Step-by-Step Solution:
#### 1. Calculate Total Purchases Each Week:
- Week 1: \( 85 + 30 + 31 = 146 \)
- Week 2: \( 110 + 22 + 23 = 155 \)
- Week 3: \( 64 + 21 + 23 = 108 \)
#### 2. Calculate Expected Soccer Ball Purchases According to the Model:
- Expected Week 1: \( 0.58 \times 146 = 84.68 \)
- Expected Week 2: \( 0.58 \times 155 = 89.9 \)
- Expected Week 3: \( 0.58 \times 108 = 62.64 \)
#### 3. Calculate Total Purchases for All Three Weeks:
- Total All Weeks: \( 146 + 155 + 108 = 409 \)
- Expected All Weeks: \( 0.58 \times 409 = 237.22 \)
#### 4. Determine Consistency:
For each week and the total, we check if the actual soccer ball purchases are within 5% of the model prediction.
- Allowed Deviation:
- For Week 1: \( 0.05 \times 146 = 7.3 \)
- For Week 2: \( 0.05 \times 155 = 7.75 \)
- For Week 3: \( 0.05 \times 108 = 5.4 \)
- For Total 3 weeks: \( 0.05 \times 409 = 20.45 \)
#### 5. Consistency Check:
- Week 1:
- Actual: 85
- Expected: 84.68
- Allowed Deviation: 7.3
- \( |85 - 84.68| = 0.32 \) which is \(\leq\) 7.3 (Consistent)
- Week 2:
- Actual: 110
- Expected: 89.9
- Allowed Deviation: 7.75
- \( |110 - 89.9| = 20.1 \) which is \(>\) 7.75 (Inconsistent)
- Week 3:
- Actual: 64
- Expected: 62.64
- Allowed Deviation: 5.4
- \( |64 - 62.64| = 1.36 \) which is \(\leq\) 5.4 (Consistent)
- Total All Weeks:
- Actual: \( 85 + 110 + 64 = 259 \)
- Expected: 237.22
- Allowed Deviation: 20.45
- \( |259 - 237.22| = 21.78 \) which is \(>\) 20.45 (Inconsistent)
### Final Classification:
| Consistent with Model | Inconsistent with Model |
|------------------------|----------------------------------|
| Week 1 results | Week 2 results |
| Week 3 results | Total of all 3 weeks' results |
You can now drag the classifications to the respective cells in the table based on the computed consistencies.
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