Question

The article "I'd Like to Buy a Vowel, Drivers Say" (USA Today, August 7,2001 ) speculates that young people prefer automobile names that consist of just numbers and/or letters that do not form a word (such as Hyundai's XG300, Mazda's 626 , and BMW's 325i). The article goes on to state that Hyundai had planned to identify the car now marketed as the XG300 with the name Concerto, until they determined that consumers hated it and that they thought XG300 sounded more "technical" and deserving of a higher price. Do the students at your school feel the same way? Describe how you would go about selecting a sample to answer this question.

Short answer

A reasonable approach to take towards this exercise would be to first define the target population and determine the sampling frame. Next, decide on a suitable sampling technique, such as simple random or stratified random sampling. Once a technique has been decided, calculate the necessary sample size considering resources and time constraints. Subsequently, carry out the sampling process and finally validate the sample to ensure it accurately represents the student population. This would result in an appropriate sample to answer the research question.

Step-by-step solution

Define the target population

The target population here is the students of the school where the survey will be conducted. This is the group about which the information is required.

Determine the sampling frame

The sampling frame could be an up-to-date list of all students in the school or a comprehensive school directory.

Choose a sampling technique

Consider using either a simple random sampling or stratified random sampling method. A simple random sampling would require assigning a unique number to each student in the school directory and using a random number generator to select students. A stratified random sampling technique would require dividing the school population into different strata (like grade level, or gender) and then applying simple random sampling within each stratum.

Decide on the sample size

The sample size must be large enough to provide a reliable representation of the school's student population. However, keep in mind feasibility issues such as time and resources.

Carry out the sampling process

Apply the chosen sampling technique to select the students and invite them to participate in the survey. Ensure the process is done ethically and respect the students' choice to participate or decline.

Validate the sample

After the sample is selected, validate it by checking if it closely represents the total student population in terms of key demographics such as grade levels, or gender.

Key concepts

Target Population

In any research, identifying the target population is the first crucial step because it defines the specific group of entities about whom the researcher wants to draw conclusions. For example, if a survey aims to discover student opinions about car model names, the target population should be the students who potentially have an interest in such topics. It's vital to make sure that the target population is very clearly defined. In our exercise case, the target population is the students at the surveyor's school. This ensures relevance, as the findings will reflect the views of the intended demographic.

To improve comprehension of the target population concept, one might consider the implications of choosing a poorly defined population, like selecting people of all ages when only young people's preferences are relevant, which can skew the results and reduce the study's accuracy.

Sampling Frame

Once the target population has been identified, the next step is to create or select a sampling frame. The sampling frame is essentially a list or database that includes all members of the target population and is used to select the sample. For instance, if the target population is students, the sampling frame might be a current student registry that includes every student who could be sampled. To maximize the effectiveness of the sampling process and reduce the sampling error, the frame should be as complete and accurate as possible. If the frame excludes some individuals or includes non-target entities, it could lead to sampling bias, where the sample is not representative of the population. In our exercise, an updated school directory would be an excellent example of a sampling frame.

Stratified Random Sampling

Stratified random sampling is an advanced sampling technique that enhances representation within the sample. It involves dividing the target population into homogenous subgroups, called strata, before the random sampling process begins.

For example, if you were selecting students to participate in a survey about car names, you might create strata based on characteristics such as grade level or declared major, since these could influence students' opinions on the subject. Within each subgroup, members are then selected randomly, often using simple random sampling. This approach helps in ensuring that each subgroup is adequately represented within the sample, thereby improving the survey's validity and accuracy. However, it requires a good understanding of the population's characteristics to create relevant strata and can be more complex and resource-intensive compared to other sampling methods.

Simple Random Sampling

Simple random sampling is one of the purest forms of probability sampling. Each member of the population has an equal chance of being included in the sample, akin to a lottery. You would first assign a unique identifier to each person in the sampling frame and then use a random number generator to pick out participants. This technique is fairly easy to understand and implement, making it popular among researchers. Nevertheless, its simplicity also comes with a downside: without stratification, simple random sampling might not capture certain subsets of the population accurately, especially if they are small but of significant interest to the study. Hence, while efficient, simple random sampling might not be the best choice for all research scenarios, especially when the population is diverse.

Sample Size Determination

Determining the sample size is a pivotal part of planning any research study. A sample should be large enough to accurately represent the population, but small enough to remain feasible in terms of resources and time. The choice of the sample size is influenced by factors such as the level of precision needed, the population size, and the expected effect size. There are statistical formulas and software that can help decide the optimal sample size based on these factors. It is important to remember that too small a sample could lead to inaccurate results that don't well represent the population (undercoverage), while too large a sample might be unnecessarily expensive and time-consuming without adding much value to the accuracy of the findings. In steps 4 and 5 of our exercise solution, the selection process and validation steps are informed by these considerations of sample size determination.