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

\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
Let's analyze the given statements one by one based on the provided survey data:

1. The survey represents quantitative data.
- Explanation: Quantitative data is numerical data that can be measured and quantified. The survey data provided here categorizes customers as either satisfied or not satisfied, which represents categorical (qualitative) data rather than quantitative data.
- Conclusion: 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.
- Explanation: Let's find the percentage of customers who are not satisfied for both Internet and Cable television services.
- For Internet:
[tex]\[ \text{Percentage of Internet customers not satisfied} = \frac{212}{2032} \approx 0.1043 \text{ or } 10.43\% \][/tex]
- For Cable television:
[tex]\[ \text{Percentage of Cable customers not satisfied} = \frac{285}{1109} \approx 0.2570 \text{ or } 25.70\% \][/tex]
- Comparing these percentages, 10.43% is less than 25.70%.
- Conclusion: This statement is False.

3. About half of the customers surveyed are cable-television customers.
- Explanation: Let's find the proportion of customers who are Cable television customers.
- Total number of customers surveyed = 3141.
- Number of Cable television customers = 1109.
- Proportion of Cable television customers:
[tex]\[ \frac{1109}{3141} \approx 0.3531 \text{ or } 35.31\% \][/tex]
- 35.31% is not approximately half (50%) of the customers.
- Conclusion: This statement is False.

4. About one-fourth of the cable-television customers are not satisfied.
- Explanation: To check this, we find the percentage of Cable television customers who are not satisfied.
- Number of Cable television customers not satisfied = 285.
- Total number of Cable television customers = 1109.
- Percentage of not satisfied Cable customers:
[tex]\[ \frac{285}{1109} \approx 0.2570 \text{ or } 25.70\% \][/tex]
- 25.70% is approximately one-fourth (25%).
- Conclusion: This statement is True.

Summary:

- Statement 1 is False.
- Statement 2 is False.
- Statement 3 is False.
- Statement 4 is True.

Thus, the true statement among the given ones is: About one-fourth of the cable-television customers are not satisfied.

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