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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

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

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.



Answer :

GinnyAnswer
To determine which statement about the two-way frequency table is true, let's analyze the given data step by step.

1. Determine the percentage of Internet customers who are not satisfied:

[tex]\[ \text{Number of Internet customers not satisfied} = 212 \][/tex]
[tex]\[ \text{Total number of Internet customers} = 2032 \][/tex]

The percentage of Internet customers who are not satisfied is:
[tex]\[ \left( \frac{212}{2032} \right) \times 100 \approx 10.43\% \][/tex]

2. Determine the percentage of Cable television customers who are not satisfied:

[tex]\[ \text{Number of Cable television customers not satisfied} = 285 \][/tex]
[tex]\[ \text{Total number of Cable television customers} = 1109 \][/tex]

The percentage of Cable television customers who are not satisfied is:
[tex]\[ \left( \frac{285}{1109} \right) \times 100 \approx 25.70\% \][/tex]

3. Determine the percentage of customers that are Cable television customers:

[tex]\[ \text{Total number of Cable television customers} = 1109 \][/tex]
[tex]\[ \text{Total number of customers surveyed} = 3141 \][/tex]

The percentage of customers who are Cable television customers is:
[tex]\[ \left( \frac{1109}{3141} \right) \times 100 \approx 35.31\% \][/tex]

Now let's evaluate each statement based on the results:

1. The survey represents quantitative data.
- This statement is incorrect as the data is categorical (satisfied/not satisfied) and is not numerical (quantitative).

2. There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied.
- This statement is incorrect because 10.43% of Internet customers are not satisfied, which is less than the 25.70% of Cable television customers who are not satisfied.

3. About half of the customers surveyed are cable-television customers.
- This statement is incorrect. The percentage of Cable television customers is approximately 35.31%, which is much lower than half (50%).

Given the analysis, none of the provided statements are true based on the calculated results.

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