To analyze the given survey results and determine which statement about the two-way frequency table is true, we'll follow these steps meticulously:
1. Calculate the percentage of Internet customers who are not satisfied:
- Number of Internet customers not satisfied: 212
- Total number of Internet customers: 2,032
- Percentage of Internet customers not satisfied:
[tex]\[
\frac{\text{Number of Internet customers not satisfied}}{\text{Total number of Internet customers}} \times 100
\][/tex]
Using the given values:
[tex]\[
\frac{212}{2032} \times 100 \approx 10.43\%
\][/tex]
2. Calculate the percentage of Cable Television customers who are not satisfied:
- Number of Cable Television customers not satisfied: 285
- Total number of Cable Television customers: 1,109
- Percentage of Cable Television customers not satisfied:
[tex]\[
\frac{\text{Number of Cable TV customers not satisfied}}{\text{Total number of Cable TV customers}} \times 100
\][/tex]
Using the given values:
[tex]\[
\frac{285}{1109} \times 100 \approx 25.70\%
\][/tex]
3. Calculate the proportion of Cable Television customers among the total surveyed customers:
- Total number of Cable Television customers: 1,109
- Overall total number of customers surveyed: 3,141
- Proportion of Cable Television customers:
[tex]\[
\frac{\text{Total number of Cable TV customers}}{\text{Overall total number of customers}}
\][/tex]
Using the given values:
[tex]\[
\frac{1109}{3141} \approx 0.353
\][/tex]
4. Evaluate the statements:
- Statement 1: "The survey represents quantitative data."
- The data provided includes counts and percentages, which are quantitative in nature. This statement appears to be true.
- Statement 2: "There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied."
- Calculated percentages:
- Internet customers not satisfied: 10.43%
- Cable Television customers not satisfied: 25.70%
- Since 10.43% (Internet) is not greater than 25.70% (Cable TV), this statement is false.
- Statement 3: "About half of the customers surveyed are cable-television customers."
- Proportion of Cable Television customers: approximately 35.3%
- Since 35.3% is significantly less than half (which would be 50% or 0.5), this statement is false.
Thus, the evaluation of the statements based on the provided analysis leads us to conclude the correct statements:
Statement 1: "The survey represents quantitative data." This is true.
Both statement 2 and statement 3 are false based on the calculations provided.
Hence, the only valid statement about the two-way frequency table is that the survey represents quantitative data.
