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An Internet and cable-television supplier surveyed a random sample of their customers. The results are shown in the table.

Satisfaction of Internet and Cable Television Customers

\begin{tabular}{|c|c|c|c|}
\hline & Satisfied & Not satisfied & Total \\
\hline Internet & 1,820 & 212 & 2,032 \\
\hline Cable television & 824 & 285 & 1,109 \\
\hline Total & 2,644 & 497 & 3,141 \\
\hline
\end{tabular}

Which statement about the two-way frequency table is true?

A. The survey represents quantitative data.
B. There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied.
C. About half of the customers surveyed are cable-television customers.
D. About one-fourth of the cable television customers are not satisfied.



Answer :

GinnyAnswer
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."

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