91Ó°ÊÓ

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 6.4 days. e. A consumer group, after testing 100 batteries of a certain brand, reported an average life of \(63 \mathrm{hr}\) of use.

Step by step solution

01

Identifying Population Characteristic or a Statistic

a. The '84%' number refers to the \(84 \%\) of all customers. This is a population characteristic since it is derived from all individuals within the group (all customers).\n\nb. The '24.1' number refers to the mean age of a sample of 100 students, not the whole university. Therefore, this is a statistic.\n\nc. The '22%' number refers to the \(22 \%\) of all vehicles, so, again, this is a population characteristic.\n\nd. The '6.4' number refers to the mean length of stay for the 10 most recent cases. It's not referring to all surgical patients, so it is a statistic.\n\ne. The '63' number is the average life of a sample of 100 batteries, not all batteries of that certain brand. So it is a statistic.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population Characteristics

When we talk about population characteristics, we refer to values or measures that describe certain aspects of an entire group or population. For instance, when a department store reports that 84% of all customers pay their bills on time, this is a population characteristic. That's because it refers to every customer using the store's credit plan, hence covering the entire population without any sampling.
Population characteristics are often viewed as the goal to understand broad trends or make predictions about entire groups.

• These characteristics are usually hard to capture completely unless a full census or comprehensive survey is done.
• They provide a benchmark or a standard for the specific attribute of interest within the population.
• Due to the inclusion of all members, population characteristics are considered precise measures.

Understanding population characteristics helps businesses and researchers draw broader and more meaningful conclusions about a group's behavior or traits.

Sample Statistics

Sample statistics are the estimates or metrics derived from a smaller part of a larger population. In our exercise, sample statistics appear when we refer to specific conditions within a smaller group. For example, the mean age of 24.1 years obtained from 100 students at a university is a sample statistic. It represents a subset of the whole student body rather than every single student.
Sample statistics are particularly useful in research because they allow for practical and efficient data analysis without needing to access the entire population.

• They help save time and resources while offering an insight into the larger population.
• Samples are selected carefully to ensure they represent the population adequately, often using techniques like random sampling.
• These statistics are critical in inferential statistics, where conclusions about a whole population are drawn from a sample.

However, because they are estimates, sample statistics may include sampling variability, meaning different samples could give slightly different results.

Statistical Analysis

Statistical analysis involves collecting, organizing, analyzing, interpreting, and presenting data to make decisions or predictions. It serves as a backbone for both understanding descriptive statistics and applying them in practical scenarios.
Through statistical analysis, differences between population characteristics and sample statistics are assessed, like understanding why the percentage of credit users paying on time (84%) might differ if sampled differently.

• Analyses help identify trends, correlations, and even causal relationships within the data.
• Includes methodologies such as hypothesis testing, regression analysis, and variance analysis.
• Ensures data is valid, reliable, and free from bias for accurate interpretations and conclusions.

Statistical analysis bridges the gap between raw data and insightful information, thus aiding in strategic planning, prediction models, and informed decision-making.

Data Interpretation

Data interpretation is the process of reviewing data with the aim of extracting meaningful information and understanding its implications. This concept is crucial for turning numbers into actionable insights. In exercises like the one described, data interpretation involves determining whether data labels should be represented as statistics or population characteristics.
For example, understanding if the 22% of vehicles that are imports applies to all registered vehicles helps in deciding marketing strategies or policy implications.

• Data interpretation requires contextual knowledge and understanding of where and how the data fits into wider contexts.
• Makes use of visual aids like charts and graphs to enhance understanding and communication of data insights.
• Helps to draw conclusions and narratives from data that are both qualitative and quantitative.

Interpreting data effectively ensures outcomes are aligned with objectives, helping organizations and individuals make informed choices.