Question

Determine whether the data collected represents a population or a sample. A researcher uses a statewide database to determine the percentage of Michigan drivers who have had an accident in the last 5 years.

Short answer

Answer: The data collected represents a population.

Step-by-step solution

Understanding Populations and Samples

A population is the complete set of all elements or individuals that we want to study, while a sample is a smaller portion of that population selected for analysis. Generally speaking, if we are analyzing data from the entire group of interest, we are working with a population. Conversely, if we are only looking at a subset of that group, we have a sample.

Determining the Data Source

In this problem, the researcher is using a statewide database to determine the percentage of Michigan drivers who have had an accident in the last 5 years. Since Michigan drivers are the entire group of interest, and the researcher is using a statewide database, it is reasonable to assume that they have access to data on all Michigan drivers, rather than just a smaller subset of those drivers.

Comparing the Data to the Population

Since the researcher is looking at data from the entire group of Michigan drivers, they are working with a population rather than a sample. If the researcher was only examining data from a subset of Michigan drivers, such as those in a specific age group or geographical region, that would be a sample.

Conclusion

The data collected represents a population since it consists of the entire group of Michigan drivers, as gathered from a statewide database.

Key concepts

Data Representation in Statistics

In statistics, how data is represented can vastly affect the outcomes of analysis and the conclusions drawn. Data can be categorical or numerical, and within these categories, it can be further classified.
For numerical data, we often use histograms, box plots, and scatter plots to visualize the information, allowing for quick identification of patterns, outliers, and distribution of the data set. Categorical data, on the other hand, is commonly represented using bar charts and pie charts, which highlight the frequency or proportion of each category.
In the educational exercise provided, the statewide database likely holds vast amounts of data related to Michigan drivers. It's crucial to represent this data correctly to convey the right message. For instance, if investigating accidents, a histogram might be used to show the distribution of accidents over time or age groups. Whereas, a pie chart could represent the proportion of types of accidents. The representation method chosen depends on the question at hand and the nature of the data collected.

Analysis of Statistical Data

Analysis is the heart of statistics. It's where patterns are discovered, hypotheses are tested, and insights are derived. There are various analytical methods, including descriptive statistics, inferential statistics, regression analysis, and hypothesis testing.
Descriptive statistics condense large datasets into summarised data points such as mean, median, mode, and standard deviation. For example, in the context of the Michigan drivers, descriptive statistics might tell us the average number of accidents per driver.
Inferential statistics, however, allows us to draw conclusions about a population based on a sample. It uses various techniques like confidence intervals and significance tests to make predictions or inferences. It should be noted that in the given exercise, since we have data on the entire population of drivers, inferential statistics might not be necessary unless comparing to another group.
Furthermore, understanding the difference between correlation and causation is vital; just because two variables move together does not mean one causes the other. This distinction becomes crucial when analyzing data to inform policy or personal decisions.

Statewide Database Utilization

The use of statewide databases provides an extensive reservoir of information for research and statistical analysis. These databases can include demographic information, health records, employment statistics, and much more.
By utilizing such a comprehensive source, a researcher can perform a full-scale analysis reflecting statewide trends and patterns. However, researchers must ensure that data is accurate, regularly updated, and reflects the demographic they're interested in studying.
In the exercise scenario involving Michigan drivers, the statewide database would likely encapsulate a complete set of records for all drivers, spanning multiple years. This presents an opportunity for longitudinal studies, which can track changes over time, and cross-sectional analyses, which provide a snapshot of a particular point in time. It’s instrumental in shaping policy decisions, seeing as the data extracted informs authorities about public safety, road conditions, and can influence regulations on driving standards.