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Magazine Chapter 1: Problem 6
The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. Would this be an enumerative or an analytic study? Explain your reasoning.
Short Answer
Expert verified
Use stratified sampling and classify as an analytic study.
Step by step solution
01
Understanding the Problem
We need to determine suitable sampling methods for calculating the average distance between the hometowns of students and their campuses across the 23 CSU campuses. Additionally, we need to decide if this exercise involves an enumerative or analytic study.
02
Considering Simple Random Sampling
In simple random sampling, every student within the CSU system has an equal chance of being selected. This requires compiling a comprehensive list of all students from all campuses, then randomly selecting participants from this list. The method is straightforward but can be logistically challenging.
03
Analyzing Stratified Sampling
Stratified sampling involves dividing the entire student population into non-overlapping groups, or strata, based on criteria such as campus or geographical location. A random sample is then taken from each stratum, ensuring that all major segments of the CSU are represented in the final sample.
04
Exploring Cluster Sampling
In cluster sampling, instead of selecting individual students, entire clusters or groups, such as campuses or classrooms, are randomly chosen. All students from the selected clusters might then be included in the sample. This method can be more cost-effective but might increase sampling error if the clusters are not homogeneous.
05
Identifying Systematic Sampling
Systematic sampling requires selecting every k-th student from an ordered list, such as alphabetical or by student ID number. This is simpler than simple random sampling and can still give us a reasonable sample if the list order does not unintentionally introduce bias.
06
Determining Enumerative vs. Analytic Study
This exercise is an analytic study because it seeks to make general inferences or predictions about the average distance from students' hometowns to their campuses using sample data. The goal is to draw conclusions that extend beyond the sample to the entire population.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Simple Random Sampling
Simple Random Sampling is a method where every member of the population has an equal chance of being selected. Imagine you want to pick students from all the CSU campuses. You need a full list of all students and then choose randomly. This method gives each student an equal opportunity to be part of the sample.
- Every student in the CSU system can be selected.
- Requires a complete list, which can be lengthy and detailed.
- Offers a neutral and unbiased selection process.
Stratified Sampling
Stratified Sampling involves dividing the overall population into subgroups or strata. These groups should be non-overlapping. For the CSU system, strata could be based on campus location or student year.
- Groups represent different segments, like campuses or geographical areas.
- Each segment provides a random sample to form the overall sample.
- Ensures all significant subgroups are included.
Cluster Sampling
Cluster Sampling selects whole groups instead of individual members. If applying this to CSU campuses, you could randomly choose a few campuses and survey all students there.
- Involves selecting entire clusters, like campuses or schools, at once.
- Reduces the penetration into individual records, simplifying logistics.
- More cost-effective but could introduce bias if clusters are not similar.
Systematic Sampling
Systematic Sampling uses a fixed interval to select participants from an ordered list. For instance, after listing students alphabetically, you might choose every 50th student.
- Begins with an organized list of the sample population.
- By sticking to a consistent interval, it creates a pseudo-randomized sample.
- Effective for ensuring spread across the list, assuming order doesn't introduce bias.
Enumerative Study
An Enumerative Study aims for conclusions confined to the data set being analyzed, typically focusing on the current conditions or specifics. It would involve assessing the specific distances within the CSU system only. However, in this case, the goal stretches beyond mere enumeration.
- Seeks to understand the data within a specific framework.
- Does not typically extend beyond the data collection scope.
- Not suitable here as we aim for broader inferences.
Analytic Study
Analytic Studies extend beyond current data, aiming to draw general conclusions or predict future trends. Here, CSU would analyze sample data to infer average distances for all students.
- Enables making predictions and finding broader trends.
- Looks beyond immediate data to impact larger sets or future events.
- Vital in scenarios like the CSU case, requiring extrapolation.
