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Answer :
To determine whether the sales results for each week and the total for 3 weeks are consistent or inconsistent with the model, we need to compare the percentage of soccer balls sold to the model's predicted percentage of 58%.
Week 1:
- Sales data: 85 soccer balls, 30 baseball bats, 31 tennis rackets.
- Total sales for Week 1: 85 + 30 + 31 = 146
- Percentage of soccer balls sold: [tex]\( \frac{85}{146} \approx 0.582 \)[/tex] or 58.2%
Since 58.2% is greater than or equal to the model's 58%, Week 1 is consistent with the model.
Week 2:
- Sales data: 110 soccer balls, 22 baseball bats, 23 tennis rackets.
- Total sales for Week 2: 110 + 22 + 23 = 155
- Percentage of soccer balls sold: [tex]\( \frac{110}{155} \approx 0.710 \)[/tex] or 71.0%
Since 71.0% is greater than the model's 58%, Week 2 is consistent with the model.
Week 3:
- Sales data: 64 soccer balls, 21 baseball bats, 23 tennis rackets.
- Total sales for Week 3: 64 + 21 + 23 = 108
- Percentage of soccer balls sold: [tex]\( \frac{64}{108} \approx 0.593 \)[/tex] or 59.3%
Since 59.3% is greater than the model's 58%, Week 3 is consistent with the model.
Total Over 3 Weeks:
- Total sales: 85 + 110 + 64 = 259 soccer balls, and 409 total items sold.
- Percentage of soccer balls sold over the 3 weeks: [tex]\( \frac{259}{409} \approx 0.633 \)[/tex] or 63.3%
Since 63.3% is greater than the model's 58%, the 3-week total is consistent with the model.
In summary, all results (Week 1, Week 2, Week 3, and the total for 3 weeks) are consistent with the model's prediction that customers choose to buy soccer balls at least 58% of the time.
Week 1:
- Sales data: 85 soccer balls, 30 baseball bats, 31 tennis rackets.
- Total sales for Week 1: 85 + 30 + 31 = 146
- Percentage of soccer balls sold: [tex]\( \frac{85}{146} \approx 0.582 \)[/tex] or 58.2%
Since 58.2% is greater than or equal to the model's 58%, Week 1 is consistent with the model.
Week 2:
- Sales data: 110 soccer balls, 22 baseball bats, 23 tennis rackets.
- Total sales for Week 2: 110 + 22 + 23 = 155
- Percentage of soccer balls sold: [tex]\( \frac{110}{155} \approx 0.710 \)[/tex] or 71.0%
Since 71.0% is greater than the model's 58%, Week 2 is consistent with the model.
Week 3:
- Sales data: 64 soccer balls, 21 baseball bats, 23 tennis rackets.
- Total sales for Week 3: 64 + 21 + 23 = 108
- Percentage of soccer balls sold: [tex]\( \frac{64}{108} \approx 0.593 \)[/tex] or 59.3%
Since 59.3% is greater than the model's 58%, Week 3 is consistent with the model.
Total Over 3 Weeks:
- Total sales: 85 + 110 + 64 = 259 soccer balls, and 409 total items sold.
- Percentage of soccer balls sold over the 3 weeks: [tex]\( \frac{259}{409} \approx 0.633 \)[/tex] or 63.3%
Since 63.3% is greater than the model's 58%, the 3-week total is consistent with the model.
In summary, all results (Week 1, Week 2, Week 3, and the total for 3 weeks) are consistent with the model's prediction that customers choose to buy soccer balls at least 58% of the time.
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