https://file.aiquickdraw.com/mathbot/file/1726640670149lz8anubv.jpg

The problem in the image asks to construct contingency tables based on total percentages, row percentages, and column percentages. The table provided breaks down student pizza preferences (Local and National) by their status (Full-Time and Part-Time). Here's the data extracted from the image:

| Pizza Preference | Full-Time | Part-Time | Total |
|------------------|-----------|-----------|-------|
| Local            | 72        | 70        | 142   |
| National         | 58        | 19        | 77    |
| Total            | 130       | 89        | 219   |

### Part (a) - Constructing a contingency table based on total percentages

We will divide each value by the grand total (219) and multiply by 100 to get the percentage of the total for each cell.

#### Table for Total Percentages:

| Pizza Preference | Full-Time (%) | Part-Time (%) | Total (%) |
|------------------|---------------|---------------|-----------|
| Local            | \(\frac{72}{219} \times 100 = 32.88\)   | \(\frac{70}{219} \times 100 = 31.96\)   | \(\frac{142}{219} \times 100 = 64.84\) |
| National         | \(\frac{58}{219} \times 100 = 26.48\)   | \(\frac{19}{219} \times 100 = 8.68\)    | \(\frac{77}{219} \times 100 = 35.16\)  |
| Total            | \(\frac{130}{219} \times 100 = 59.36\)  | \(\frac{89}{219} \times 100 = 40.64\)   | 100.00     |

Would you like me to continue with row and column percentages or explain any part of this further?

Here are 5 related questions you may want to explore:
1. How are row percentages different from column percentages?
2. What do contingency tables reveal about the relationship between two variables?
3. How would you calculate expected counts for a chi-square test using this table?
4. How can we visually represent the data in a contingency table?
5. What is the interpretation of each percentage in the contingency table?

**Tip**: Always ensure that your percentages in a contingency table sum to 100% for the appropriate category (row, column, or total).

A national pizza chain seeks to expand and open a store in the small town that is home to a regional public university. Students at that school are known for being customers of the local pizza restaurant, an independent restaurant, and the pizza chain conducts a survey of students to determine pizza preferences. The chain selects a sample of 219 students attending the university. The results are summarized in the accompanying table.

Explore the contingency table showing pizza preferences (Local and National) among full-time and part-time students at a public university. Learn how to calculate total, row, and column percentages for the 219 surveyed students. A great resource for students studying introductory statistics.

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