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I can help you with the table and the question in the image! Let's break down the task.

The problem involves constructing two tables based on percentages:

1. **Row Percentages**: The task asks you to complete a table that reflects the percentage of full-time and part-time students who prefer "Local" and "National" pizza chains.

2. **Column Percentages**: The second table needs to be based on column percentages, which means showing the breakdown of pizza preferences (Local vs. National) for full-time and part-time students.

Here's the given data from the table in the image:

- **Local preference**:
  - Full-time: 72
  - Part-time: 70
  - Total (Local): 142
- **National preference**:
  - Full-time: 58
  - Part-time: 19
  - Total (National): 77
- **Grand total** (students surveyed): 219
  - Full-time: 130
  - Part-time: 89

### Part (a): Constructing the Tables

#### Row Percentages
You can calculate the row percentages by dividing the number of students in each category by the row total and then multiplying by 100.

For example, for full-time students who prefer "Local," the calculation is:
\[
\frac{72}{130} \times 100 \approx 55.38\%
\]

Similarly, for part-time students who prefer "Local":
\[
\frac{70}{89} \times 100 \approx 78.65\%
\]

I'll calculate the rest of the percentages for both tables and provide you with more detailed conclusions. Let's go ahead and calculate these!### Part (a): Constructed Tables

#### Row Percentages (Based on Student Status)
- **Local Preference**:
  - Full-time: 55.38%
  - Part-time: 78.65%
  - Total: 100%

- **National Preference**:
  - Full-time: 44.62%
  - Part-time: 21.35%
  - Total: 100%

#### Column Percentages (Based on Pizza Preference)
- **Local Pizza Preference**:
  - Full-time: 50.70%
  - Part-time: 49.30%
  - Total: 100%

- **National Pizza Preference**:
  - Full-time: 75.32%
  - Part-time: 24.68%
  - Total: 100%

### Part (b): Conclusions
- Full-time students were **more likely** to prefer **National** pizza (75.32% prefer National).
- Part-time students were **more likely** to prefer **Local** pizza (78.65% prefer Local).

Would you like further clarification or details on these results?

Here are 5 related questions to explore:
1. How do column and row percentages help in decision-making for market analysis?
2. How might the pizza chain use this data to strategize their marketing campaign?
3. Could there be other factors influencing pizza preferences besides student status?
4. What statistical methods could be used to determine the significance of these preferences?
5. How would changing the sample size affect the percentage calculations?

**Tip**: When analyzing data, always look at both row and column percentages for a complete picture of relationships between variables.

A national pizza chain seeks to expand and open a store in the small town that is home to a regional public university. The pizza chain conducts a survey of 219 students to determine pizza preferences. The survey data is categorized by full-time and part-time students preferring either a local or national pizza. You are asked to construct two tables: one based on row percentages and the other on column percentages, and to interpret the conclusions.

This statistics problem involves constructing row and column percentage tables to analyze pizza preferences among full-time and part-time university students. Explore how to calculate row and column percentages based on survey data and interpret conclusions from the analysis. Suitable for Grades 10-12.

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