To determine which statement about the given two-way frequency table is true, let's analyze the data presented in the table:
### Table Recap:
| | Satisfied | Not satisfied | Total |
|---------------------|-----------|---------------|--------|
| Internet | 1,820 | 212 | 2,032 |
| Cable television| 824 | 285 | 1,109 |
| Total | 2,644 | 497 | 3,141 |
### Step-by-Step Analysis:
#### 1. The survey represents quantitative data.
- Assessment: The survey results deal with categorical data, not numerical quantities. It tracks customer satisfaction (a category) rather than measuring some quantity. This statement is false.
#### 2. There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied.
- Calculation:
- Percentage of Internet customers who are not satisfied:
[tex]\[
\left(\frac{212}{2,032}\right) \times 100 \approx 10.43\%
\][/tex]
- Percentage of Cable television customers who are not satisfied:
[tex]\[
\left(\frac{285}{1,109}\right) \times 100 \approx 25.70\%
\][/tex]
- Assessment: The percentage of Internet customers who are not satisfied (10.43%) is less than the percentage of cable television customers who are not satisfied (25.70%). This statement is false.
#### 3. About half of the customers surveyed are cable-television customers.
- Calculation:
- Percentage of total customers who are cable television customers:
[tex]\[
\left(\frac{1,109}{3,141}\right) \times 100 \approx 35.31\%
\][/tex]
- Assessment: Approximately 35.31% of the total customers surveyed are cable-television customers, which is not about half. This statement is false.
#### 4. About one-fourth of the cable television customers are not satisfied.
- Calculation:
- Percentage of cable television customers who are not satisfied:
[tex]\[
\left(\frac{285}{1,109}\right) \times 100 \approx 25.70\%
\][/tex]
- Assessment: Approximately 25.70% of cable television customers are not satisfied, which is about one-fourth. This statement is true.
### Conclusion:
Based on the analysis, the true statement about the two-way frequency table is:
"About one-fourth of the cable television customers are not satisfied."
