Question

For the following reports about statistical studies, identify the following items (if possible). If you can't tell, then say so-this often happens when we read about a survey. a) The population b) The population parameter of interest c) The sampling frame d) The sample e) The sampling method, including whether or not randomization was employed f) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest State police set up a roadblock to estimate the percentage of cars with up-to- date registration, insurance, and safety inspection stickers. They usually find problems with about \(10 \%\) of the cars they stop.

Short answer

Population: All cars; Parameter: Percentage of compliant cars; Sample: Cars stopped at roadblock; Method: Convenience sampling; Bias: Location bias; Generalization issues exist.

Step-by-step solution

Identify the Population

The population in this scenario would be all the cars on the road, as the interest is in the cars' compliance with registration, insurance, and safety inspection within this broad group.

Determine the Population Parameter of Interest

The population parameter of interest is the percentage of cars with up-to-date registration, insurance, and safety inspection stickers within the total population of cars.

Identify the Sampling Frame

The sampling frame appears to be the subset of cars that travel through the roadblock, as only these cars are included in the study.

Define the Sample

The sample consists of the cars that were actually stopped and checked at the roadblock for up-to-date registration, insurance, and safety inspection stickers.

Examine the Sampling Method

The sampling method employed is a form of convenience sampling as only cars passing through a specific location (the roadblock) are sampled. We cannot definitively say randomization was used.

Identify Potential Sources of Bias and Generalization Issues

Potential sources of bias include location bias, as the roadblock only samples cars passing through that specific location, possibly excluding cars from other areas. This could affect the generalizability of the results to the entire population of cars.

Key concepts

Population Parameter

A population parameter is a value that gives information about a particular characteristic of an entire population. In the context of statistical studies, it is the inherent trait or measure you are interested in investigating. For instance, if a study is examining cars, a common population parameter might be the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. This parameter tells researchers important information about compliance across the full collection of interest, whether it be a town, city, or even a national level.

Understanding the population parameter helps to define the goal of the survey or experiment. In our example, the percentage provides insight into regulatory compliance. It establishes not only a target measure but also helps to formulate questions and interpret how representative a sample is regarding the population.

Sampling Method

The sampling method is a strategy used to select elements from a population to be included in a sample. There are various sampling methods such as random sampling, stratified sampling, and convenience sampling, each bringing different advantages and drawbacks.

In statistical surveys, employing a robust sampling method is crucial. For example, convenience sampling, while easy to administer and cost-effective, may not properly represent a broader population. This can be seen in the roadblock study, as only cars passing through a specific location were sampled. This method might unintentionally exclude vehicles from other roads or areas, limiting the study’s ability to generalize findings.

Choosing an appropriate sampling method often involves balancing practicality with the need for unbiased representation to ensure accurate and useful results.

Bias in Surveys

Bias in surveys occurs when the collected data does not accurately represent the true population characteristics. This can arise from several factors during the survey design or implementation, impacting the validity of any conclusions drawn.

Common types of bias include:

• Location Bias: When the sample only includes specific locations, as in our roadblock study, other locations are left unrepresented.
• Selection Bias: If certain groups are systematically excluded or included, the findings may not reliably reflect the broader population.

These biases hinder the ability to generalize results. For instance, the police roadblock might consistently target high-traffic areas, thus missing the compliance status of cars on less frequented roads.

To minimize bias, researchers can use random sampling techniques and ensure their sampling frame includes a wide range of data points. Recognizing and adjusting for possible biases during the planning stages of a study enhances both credibility and reliability.