Answer :
To analyze the data, let's walk through the calculations to determine the correct statement based on the survey results:
1. Percentage of Internet customers who are not satisfied:
[tex]\[ \text{Percentage of Internet customers not satisfied} = \left( \frac{\text{Internet Not Satisfied}}{\text{Internet Total}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ = \left( \frac{212}{2032} \right) \times 100 \approx 10.43\% \][/tex]
2. Percentage of Cable television customers who are not satisfied:
[tex]\[ \text{Percentage of Cable customers not satisfied} = \left( \frac{\text{Cable Not Satisfied}}{\text{Cable Total}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ = \left( \frac{285}{1109} \right) \times 100 \approx 25.70\% \][/tex]
3. Percentage of customers who are cable-television customers:
[tex]\[ \text{Percentage of Cable customers} = \left( \frac{\text{Cable Total}}{\text{Overall Total}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ = \left( \frac{1109}{3141} \right) \times 100 \approx 35.31\% \][/tex]
### Evaluation of the Statements:
1. The survey represents quantitative data.
- This statement is false because the data collected (satisfied or not satisfied) is categorical rather than 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 false. The percentage of Cable television customers not satisfied (25.70%) is greater than the percentage of Internet customers not satisfied (10.43%).
3. About half of the customers surveyed are cable-television customers.
- This statement is false. The percentage of Cable customers is approximately 35.31%, which is significantly less than half.
Thus, based on the provided data and calculations, none of the statements given are true.
1. Percentage of Internet customers who are not satisfied:
[tex]\[ \text{Percentage of Internet customers not satisfied} = \left( \frac{\text{Internet Not Satisfied}}{\text{Internet Total}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ = \left( \frac{212}{2032} \right) \times 100 \approx 10.43\% \][/tex]
2. Percentage of Cable television customers who are not satisfied:
[tex]\[ \text{Percentage of Cable customers not satisfied} = \left( \frac{\text{Cable Not Satisfied}}{\text{Cable Total}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ = \left( \frac{285}{1109} \right) \times 100 \approx 25.70\% \][/tex]
3. Percentage of customers who are cable-television customers:
[tex]\[ \text{Percentage of Cable customers} = \left( \frac{\text{Cable Total}}{\text{Overall Total}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ = \left( \frac{1109}{3141} \right) \times 100 \approx 35.31\% \][/tex]
### Evaluation of the Statements:
1. The survey represents quantitative data.
- This statement is false because the data collected (satisfied or not satisfied) is categorical rather than 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 false. The percentage of Cable television customers not satisfied (25.70%) is greater than the percentage of Internet customers not satisfied (10.43%).
3. About half of the customers surveyed are cable-television customers.
- This statement is false. The percentage of Cable customers is approximately 35.31%, which is significantly less than half.
Thus, based on the provided data and calculations, none of the statements given are true.
