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Answer :
To determine if the weekly and total results are consistent or inconsistent with the store owner's model, let's break down the problem step by step.
1. Understanding the Model:
- The model states that customers choose to buy soccer balls 58% of the time.
2. Gathering the Data:
- We have three weeks' worth of data on the number of soccer balls, baseball bats, and tennis rackets sold:
- 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
3. Calculating Total Purchases:
- We sum the data for each week to get the total purchases:
- Total purchases = (85 + 110 + 64) soccer balls, (30 + 22 + 21) baseball bats, (31 + 23 + 23) tennis rackets
- Total purchases = 259 soccer balls, 73 baseball bats, and 77 tennis rackets.
4. Calculating the Total Number of Items Purchased:
- Total items purchased overall = 259 soccer balls + 73 baseball bats + 77 tennis rackets = 409 items.
5. Checking Consistency for Each Week and Total:
- We need to see if the results are consistent with 58% of purchases being soccer balls.
- We’ll allow a margin of error of ±5% (which is common in statistical models).
6. Week-by-Week and Total Calculations:
- Week 1:
- Total purchases = 85 + 30 + 31 = 146 items.
- Expected soccer balls = 0.58 146 = 84.68.
- Allowable margin = 0.05 146 = 7.3.
- Observed soccer balls = 85.
- Since 85 is within (84.68 ± 7.3), the result is consistent.
- Week 2:
- Total purchases = 110 + 22 + 23 = 155 items.
- Expected soccer balls = 0.58 155 = 89.9.
- Allowable margin = 0.05 155 = 7.75.
- Observed soccer balls = 110.
- Since 110 is not within (89.9 ± 7.75), the result is inconsistent.
- Week 3:
- Total purchases = 64 + 21 + 23 = 108 items.
- Expected soccer balls = 0.58 108 = 62.64.
- Allowable margin = 0.05 108 = 5.4.
- Observed soccer balls = 64.
- Since 64 is within (62.64 ± 5.4), the result is consistent.
- Total (All 3 Weeks):
- Total purchases = 409 items.
- Expected soccer balls = 0.58 409 = 237.22.
- Allowable margin = 0.05 409 = 20.45.
- Observed soccer balls = 259.
- Since 259 is not within (237.22 ± 20.45), the result is inconsistent.
7. Summary:
- Week 1: Consistent
- Week 2: Inconsistent
- Week 3: Consistent
- Total for all weeks: Inconsistent
Therefore, the classification of the results based on the model is:
- Total of all 3 weeks' results: Inconsistent
- Week 1 results: Consistent
- Week 2 results: Inconsistent
- Week 3 results: Consistent
1. Understanding the Model:
- The model states that customers choose to buy soccer balls 58% of the time.
2. Gathering the Data:
- We have three weeks' worth of data on the number of soccer balls, baseball bats, and tennis rackets sold:
- 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
3. Calculating Total Purchases:
- We sum the data for each week to get the total purchases:
- Total purchases = (85 + 110 + 64) soccer balls, (30 + 22 + 21) baseball bats, (31 + 23 + 23) tennis rackets
- Total purchases = 259 soccer balls, 73 baseball bats, and 77 tennis rackets.
4. Calculating the Total Number of Items Purchased:
- Total items purchased overall = 259 soccer balls + 73 baseball bats + 77 tennis rackets = 409 items.
5. Checking Consistency for Each Week and Total:
- We need to see if the results are consistent with 58% of purchases being soccer balls.
- We’ll allow a margin of error of ±5% (which is common in statistical models).
6. Week-by-Week and Total Calculations:
- Week 1:
- Total purchases = 85 + 30 + 31 = 146 items.
- Expected soccer balls = 0.58 146 = 84.68.
- Allowable margin = 0.05 146 = 7.3.
- Observed soccer balls = 85.
- Since 85 is within (84.68 ± 7.3), the result is consistent.
- Week 2:
- Total purchases = 110 + 22 + 23 = 155 items.
- Expected soccer balls = 0.58 155 = 89.9.
- Allowable margin = 0.05 155 = 7.75.
- Observed soccer balls = 110.
- Since 110 is not within (89.9 ± 7.75), the result is inconsistent.
- Week 3:
- Total purchases = 64 + 21 + 23 = 108 items.
- Expected soccer balls = 0.58 108 = 62.64.
- Allowable margin = 0.05 108 = 5.4.
- Observed soccer balls = 64.
- Since 64 is within (62.64 ± 5.4), the result is consistent.
- Total (All 3 Weeks):
- Total purchases = 409 items.
- Expected soccer balls = 0.58 409 = 237.22.
- Allowable margin = 0.05 409 = 20.45.
- Observed soccer balls = 259.
- Since 259 is not within (237.22 ± 20.45), the result is inconsistent.
7. Summary:
- Week 1: Consistent
- Week 2: Inconsistent
- Week 3: Consistent
- Total for all weeks: Inconsistent
Therefore, the classification of the results based on the model is:
- Total of all 3 weeks' results: Inconsistent
- Week 1 results: Consistent
- Week 2 results: Inconsistent
- Week 3 results: Consistent
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