Question

A consumer group conducts crash tests of new model cars. To determine the severity of damage to 2013 Toyota Camrys resulting from a 10 -mph crash into a concrete wall, the research group tests six cars of this type and assesses the amount of damage. Describe the population and sample for this problem.

Short answer

The population in this case is all of the 2013 Toyota Camrys. The sample is the set of six 2013 Toyota Camrys that were crash-tested by the research group.

Step-by-step solution

Identify the Population

In the given problem, the population would be all 2013 Toyota Camrys. This is because in statistics, a population is a complete set that includes all members (subjects) to be studied. So, for this problem, the population are all 2013 Toyota Camrys existing.

Identify the Sample

The sample, on the other hand, is a subset of the population, which in this case is represented by the six 2013 Toyota Camrys that were crash-tested by the consumer group. The sample is the set of subjects selected from the population for study or testing.

Key concepts

Statistical Population

Understanding the concept of a statistical population is crucial for anyone delving into the world of statistics. In the most general sense, a statistical population is the complete set of items or individuals that we want to study and make inferences about. When we refer to 'population' in statistics, we're not just talking about people; it could also encompass animals, objects, or events.

For instance, if a car manufacturer or a consumer group is interested in the safety features of a specific car model, like the 2013 Toyota Camry, then all of the 2013 Camrys manufactured constitute the statistical population. This group includes every single 2013 Camry out there, regardless of location or condition. Analyzing the entire population can often be impractical or impossible due to time, cost, or logistical reasons. That's where the concept of a sample comes into play, which we use to estimate or predict characteristics of the whole population.

Statistical Sample

A statistical sample, in essence, is a small, manageable piece of a much larger statistical population. The purpose of selecting a sample is to make observations or conduct experiments on this smaller group, which can then be generalized to the larger population. This is central to the practice of statistics, as it allows for the collection of data and inference-making without needing to involve every single member of the population.

In the context of the exercise, the six 2013 Toyota Camrys that underwent crash testing represent the sample. These cars were specifically selected to provide insights into the larger group—every 2013 Camry ever made. It's vital to ensure that the sample is representative of the population for the results to be accurate when generalized. This is one of the key challenges statisticians face: ensuring that their sample accurately reflects the diversity and characteristics of the entire population.

Crash Test Analysis

Crash test analysis is a methodical procedure widely employed by automotive companies and consumer safety groups to assess the safety and durability of vehicles. By conducting controlled collisions with barriers such as concrete walls, these tests simulate real-world accidents to understand how a vehicle and its safety systems perform under stress.

This information is invaluable for both improving car safety features and informing consumers about potential risks. In a crash test analysis like the one described in our exercise, experts not only collect data on the damage sustained by the car's structure but also study the impact on crash test dummies to understand the potential injuries to passengers. By analyzing the outcomes of such crash tests on a sample of 2013 Toyota Camrys, researchers can draw conclusions about the safety of this car model in low-speed collisions for the whole population of Camrys.

Data Collection Methods

Data collection is a systematic approach to gathering information from a variety of sources to create a complete set of data which can then be used for statistical analysis. There are numerous methods for collecting data, and the choice of method can significantly affect the quality of the results. Some common methods include surveys, experiments, observations, and the use of existing data sources.

In the exercise scenario, the data collection method used is an experiment involving crash testing vehicles. This approach is highly controlled, with specific conditions set to measure the outcomes accurately. Another component to consider is data quality; ensuring that the data is reliable and valid is paramount for accurate statistical analysis. The methods chosen for data collection should align with the research objectives and provide the most useful and relevant information possible.