An Internet and cable-television supplier surveyed a random sample of their customers. The results are shown in the table.
Satisfaction of Internet and CableTelevision Customers
| | Satisfied | Not satisfied | Total |
| :---------------- | :-------- | :------------ | :---- |
| Internet | 1,820 | 212 | 2,032 |
| Cable television | 824 | 285 | 1,109 |
| Total | 2,644 | 497 | 3,141 |
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 (1)
Calculate the percentage of Internet customers not satisfied: 2032 212 × 100 ≈ 10.43% .
Calculate the percentage of Cable TV customers not satisfied: 1109 285 × 100 ≈ 25.70% .
Calculate the percentage of Cable TV customers surveyed: 3141 1109 × 100 ≈ 35.31% .
The statement 'About one-fourth of the cable-television customers are not satisfied' is true, since 25.70% ≈ 25% .
About one-fourth of the cable-television customers are not satisfied.
Explanation
Analyze the problem We are given a two-way frequency table showing the satisfaction of Internet and Cable Television customers. We need to determine which of the given statements is true.
Check the first statement First, let's analyze the statement: 'The survey represents quantitative data.' Quantitative data is numerical data, while this survey collects categorical data (satisfied or not satisfied). Thus, this statement is false.
Check the second statement Next, let's analyze the statement: 'There is a greater percentage of Internet customers who are not satisfied than cable television customers who are not satisfied.'
We calculate the percentage of Internet customers who are not satisfied: 2032 212 × 100 ≈ 10.43%
We calculate the percentage of Cable Television customers who are not satisfied: 1109 285 × 100 ≈ 25.70%
Since 10.43% < 25.70% , this statement is false.
Check the third statement Now, let's analyze the statement: 'About half of the customers surveyed are cable-television customers.'
We calculate the percentage of customers surveyed who are cable-television customers: 3141 1109 × 100 ≈ 35.31%
Since 35.31% is not approximately 50% , this statement is false.
Check the fourth statement Finally, let's analyze the statement: 'About one-fourth of the cable-television customers are not satisfied.'
We calculate the percentage of cable-television customers who are not satisfied: 1109 285 × 100 ≈ 25.70%
One-fourth is 25% . Since 25.70% is approximately 25% , this statement is true.
Conclusion Therefore, the true statement is: About one-fourth of the cable-television customers are not satisfied.
Examples
Two-way frequency tables are commonly used in market research to analyze customer satisfaction across different services or products. For example, a company might survey customers about their satisfaction with both their internet and phone services. The results can be organized in a table like the one above to identify areas where the company is performing well and areas that need improvement. By calculating percentages, the company can compare satisfaction levels across different services and make informed decisions about resource allocation and service improvements. This helps the company to better understand customer needs and improve overall customer satisfaction.
