Answer :
Let's analyze each statement one by one based on the data provided and calculated results:
### Statement 1: "The survey represents quantitative data."
- The data in the table is categorical (satisfied, not satisfied) and numerical (counts of customers in each category). While the numerical values provide the counts of customers, the satisfaction data itself is categorical, not quantitative.
### Statement 2: "There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied."
- The rate of not satisfied Internet customers is:
[tex]\[ \text{Rate of Internet not satisfied} = 0.1043 \text{ (approx. 10.43%)} \][/tex]
- The rate of not satisfied cable television customers is:
[tex]\[ \text{Rate of Cable not satisfied} = 0.257 \text{ (approx. 25.70%)} \][/tex]
- Comparing the two rates, the percentage of not satisfied cable television customers is greater than that of Internet customers. Therefore, this statement is false.
### Statement 3: "About half of the customers surveyed are cable-television customers."
- The total number of customers surveyed is:
[tex]\[ 3,141 \][/tex]
- The number of cable-television customers is:
[tex]\[ 1,109 \][/tex]
- The percentage of cable-television customers is:
[tex]\[ \frac{1,109}{3,141} = 0.353 \text{ (approx. 35.31%)} \][/tex]
- 35.31% is not "about half" of the total customers, thus this statement is false.
### Statement 4: "About one-fourth of the cable-television customers are not satisfied."
- The number of not satisfied cable-television customers is:
[tex]\[ 285 \][/tex]
- The total number of cable-television customers is:
[tex]\[ 1,109 \][/tex]
- The percentage of not satisfied cable-television customers is:
[tex]\[ \frac{285}{1,109} = 0.257 \text{ (approx. 25.70%)} \][/tex]
- 25.70% is very close to one-fourth (25%), making this statement true.
### Conclusion:
The true statement among the given options is:
- "About one-fourth of the cable-television customers are not satisfied."
### Statement 1: "The survey represents quantitative data."
- The data in the table is categorical (satisfied, not satisfied) and numerical (counts of customers in each category). While the numerical values provide the counts of customers, the satisfaction data itself is categorical, not quantitative.
### Statement 2: "There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied."
- The rate of not satisfied Internet customers is:
[tex]\[ \text{Rate of Internet not satisfied} = 0.1043 \text{ (approx. 10.43%)} \][/tex]
- The rate of not satisfied cable television customers is:
[tex]\[ \text{Rate of Cable not satisfied} = 0.257 \text{ (approx. 25.70%)} \][/tex]
- Comparing the two rates, the percentage of not satisfied cable television customers is greater than that of Internet customers. Therefore, this statement is false.
### Statement 3: "About half of the customers surveyed are cable-television customers."
- The total number of customers surveyed is:
[tex]\[ 3,141 \][/tex]
- The number of cable-television customers is:
[tex]\[ 1,109 \][/tex]
- The percentage of cable-television customers is:
[tex]\[ \frac{1,109}{3,141} = 0.353 \text{ (approx. 35.31%)} \][/tex]
- 35.31% is not "about half" of the total customers, thus this statement is false.
### Statement 4: "About one-fourth of the cable-television customers are not satisfied."
- The number of not satisfied cable-television customers is:
[tex]\[ 285 \][/tex]
- The total number of cable-television customers is:
[tex]\[ 1,109 \][/tex]
- The percentage of not satisfied cable-television customers is:
[tex]\[ \frac{285}{1,109} = 0.257 \text{ (approx. 25.70%)} \][/tex]
- 25.70% is very close to one-fourth (25%), making this statement true.
### Conclusion:
The true statement among the given options is:
- "About one-fourth of the cable-television customers are not satisfied."
