To determine if the results for each category are consistent or inconsistent with the owner's model, we need to compare the percentage of soccer balls sold each week to the expected [tex]$58\%$[/tex] of total sales, with a margin of error of [tex]$\pm 5\%$[/tex].
1. Week 1 Results:
- Soccer Balls: 85
- Baseball Bats: 30
- Tennis Rackets: 31
- Total Sales for Week 1: [tex]$85 + 30 + 31 = 146$[/tex]
- Percentage of Soccer Balls Sold in Week 1: [tex]$\frac{85}{146} \approx 0.5822 \approx 58.22\%$[/tex]
Since [tex]$58.22\%$[/tex] is within the [tex]$53\%$[/tex] to [tex]$63\%$[/tex] range (accounting for the [tex]$\pm 5\%$[/tex] margin), Week 1 is consistent with the model.
2. Week 2 Results:
- Soccer Balls: 110
- Baseball Bats: 22
- Tennis Rackets: 23
- Total Sales for Week 2: [tex]$110 + 22 + 23 = 155$[/tex]
- Percentage of Soccer Balls Sold in Week 2: [tex]$\frac{110}{155} \approx 0.7097 \approx 71.0\%$[/tex]
Since [tex]$71.0\%$[/tex] is outside the [tex]$53\%$[/tex] to [tex]$63\%$[/tex] range, Week 2 is inconsistent with the model.
3. Week 3 Results:
- Soccer Balls: 64
- Baseball Bats: 21
- Tennis Rackets: 23
- Total Sales for Week 3: [tex]$64 + 21 + 23 = 108$[/tex]
- Percentage of Soccer Balls Sold in Week 3: [tex]$\frac{64}{108} \approx 0.5926 \approx 59.26\%$[/tex]
Since [tex]$59.26\%$[/tex] is within the [tex]$53\%$[/tex] to [tex]$63\%$[/tex] range, Week 3 is consistent with the model.
4. Total of All 3 Weeks:
- Total Soccer Balls Sold: [tex]$85 + 110 + 64 = 259$[/tex]
- Total Baseball Bats Sold: [tex]$30 + 22 + 21 = 73$[/tex]
- Total Tennis Rackets Sold: [tex]$31 + 23 + 23 = 77$[/tex]
- Total Sales for All Weeks: [tex]$259 + 73 + 77 = 409$[/tex]
- Percentage of Soccer Balls Sold in All Weeks: [tex]$\frac{259}{409} \approx 0.6330 \approx 63.3\%$[/tex]
Since [tex]$63.3\%$[/tex] is outside the [tex]$53\%$[/tex] to [tex]$63\%$[/tex] range, the total of all 3 weeks is inconsistent with the model.
Therefore, the classification of results according to the model is:
\begin{tabular}{|l|l|}
\hline \begin{tabular}{c}
Consistent with \\
Model
\end{tabular} & \begin{tabular}{c}
Inconsistent with \\
Model
\end{tabular} \\
\hline Week 1 results & Week 2 results \\
Week 3 results & Total of all 3 weeks \\
& \\
\hline
\end{tabular}
