Answered

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 evaluate which statement about the survey results is true, let's analyze the given data in detailed steps:

### Data Overview
The table provides satisfaction data for both Internet and Cable television customers:

| | 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. Calculate the percentage of not satisfied customers for Internet customers:
- Total Internet customers: 2,032
- Internet customers who are not satisfied: 212
- Percentage = (Not satisfied / Total Internet customers) 100
- Percentage = (212 / 2,032) 100 = 10.4331%

2. Calculate the percentage of not satisfied customers for Cable TV customers:
- Total Cable TV customers: 1,109
- Cable TV customers who are not satisfied: 285
- Percentage = (Not satisfied / Total Cable TV customers) 100
- Percentage = (285 / 1,109) 100 = 25.6988%

3. Calculate the percentage of surveyed customers who are Cable TV customers:
- Total surveyed customers: 3,141
- Cable TV customers: 1,109
- Percentage = (Cable TV customers / Total surveyed customers) 100
- Percentage = (1,109 / 3,141) 100 = 35.3072%

4. Calculate the percentage of not satisfied customers for Cable TV out of the Cable TV customers:
- As previously calculated, the percentage not satisfied: 25.6988%

### Evaluating Statements

1. The survey represents quantitative data.
- This statement is false. The survey data shows qualitative (categorical) data about satisfaction levels rather than quantitative data.

2. There is a greater percentage of Internet customers who are not satisfied than Cable television customers who are not satisfied.
- This statement is false. The percentage of not satisfied customers is higher for Cable TV (25.6988%) compared to Internet customers (10.4331%).

3. About half of the customers surveyed are Cable television customers.
- This statement is false. Only about 35.3072% of the customers surveyed are Cable TV customers, which is considerably less than half.

4. About one-fourth of the Cable television customers are not satisfied.
- This statement is true. The percentage of Cable TV customers who are not satisfied is 25.6988%, which is approximately one-fourth.

Conclusion: The true statement is:
- "About one-fourth of the Cable television customers are not satisfied."