Question

For each of the following statements, identify the number that appears in boldface type as the value of either a population characteristic or a statistic: a. A department store reports that \(84 \%\) of all customers who use the store's credit plan pay their bills on time. b. A sample of 100 students at a large university had a mean age of 24.1 years. c. The Department of Motor Vehicles reports that \(22 \%\) of all vehicles registered in a particular state are imports. d. A hospital reports that, based on the 10 most recent cases, the mean length of stay for surgical patients is \(\mathbf{6} . \mathbf{4}\) days. e. A consumer group, after testing 100 batteries of a certain brand, reported an average life of \(\mathbf{6 3}\) hours of use.

Short answer

a: Population characteristic (\(84 \%\) of customers), b: Statistic (mean age of \(24.1\) years), c: Population characteristic (\(22 \%\) of registered vehicles), d: Statistic (mean stay of \(6.4\) days), e: Statistic (average life of \(63\) hours)

Step-by-step solution

Identify and categorize statement A

The statement is 'A department store reports that \(84 \%\) of all customers who use the store's credit plan pay their bills on time.' Here, the department store is referring to all of its customers who use the store's credit plan, indicating that it is referring to the entire population. Therefore, \(84 \%\) is a population characteristic.

Identify and categorize statement B

The statement is 'A sample of 100 students at a large university had a mean age of 24.1 years.' In this case, the data is taken from a sample (100 students) from potentially a larger population (all students at the university). So, \(24.1\) years is a statistic.

Identify and categorize statement C

The statement is 'The Department of Motor Vehicles reports that \(22 \%\) of all vehicles registered in a particular state are imports.' Here, the Department of Motor Vehicles refers to all the vehicles registered in a state, signifying a population. Consequently, \(22 \%\) is a population characteristic.

Identify and categorize statement D

The statement is 'A hospital reports that, based on the 10 most recent cases, the mean length of stay for surgical patients is \(6.4\) days.' Here, the data is taken from a sample (10 most recent cases) of a larger population (all surgical patients at the hospital). Hence, \(6.4\) days is a statistic.

Identify and categorize statement E

The statement is 'A consumer group, after testing 100 batteries of a certain brand, reported an average life of \(63\) hours of use.' Since the statement refers to a sample (100 batteries) of a larger population (all batteries of a certain brand), \(63\) hours is a statistic.