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91Ó°ÊÓ

In Problems 11-22, identify the type of sampling used. To obtain students' opinions about proposed changes to course registration procedures, the administration of a small college asked for faculty volunteers who were willing to administer a survey in one of their classes. Twenty-three faculty members volunteered. Each faculty member gave the survey to all the students in one course of their choosing. Would this sampling method be considered a cluster sample? Why or why not?

Short Answer

Expert verified
Yes, this is cluster sampling because classes were chosen as clusters, and all students within those chosen clusters were surveyed.

Step by step solution

01

Understanding the Problem

Read the problem carefully and identify the key elements. The problem involves determining the type of sampling used when faculty administer a survey about course registration changes.
02

Identifying the Sampling Method

Determine how the sample was obtained. In this case, faculty members volunteered to participate and chose one of their classes to administer the survey to all students in that class.
03

Defining Cluster Sampling

Cluster sampling involves dividing the population into groups (clusters) and then randomly selecting some of these clusters. Every individual within the chosen clusters is then surveyed.
04

Comparing the Sampling Method

Compare the described sampling method to the definition of cluster sampling. In the problem, faculty members chose one of their classes and surveyed all students in that class. This means the population was divided into classes (clusters), and specific clusters (classes) were chosen by the faculty.
05

Conclusion

Conclude that the sampling method used is indeed cluster sampling because the faculty members surveyed all students within the clusters (chosen classes) they selected.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cluster Sampling
Cluster sampling is a popular technique in statistics for gathering data from a population. It involves the division of the population into groups, known as clusters. These clusters are typically groups of similar characteristics. Once the clusters are defined, researchers randomly select a few of these clusters. Every individual within the selected clusters is then surveyed.
This method is particularly useful when the population is large and widely spread across geographic areas. By concentrating on specific clusters, researchers can efficiently collect data without having to survey the entire population, which saves time and resources.
In the exercise, faculty members chose one of their classes and surveyed all students in that class. Each class is a cluster, and the sampling method aligns perfectly with the principles of cluster sampling.
Survey Methodology
Survey methodology involves the strategic process of gathering data from a predefined group. It’s essential to ensure that the survey methodology is sound to obtain reliable data.
Key components include creating a clear survey design, selecting an appropriate sample, and developing precise questions. Proper implementation of all these steps ensures accurate data collection.
In our exercise, the administration asked faculty members to voluntarily administer the survey to their chosen classes. Although not random, faculty members administered the survey in a structured environment, thus ensuring the high integrity of data collected from each cluster.
Types of Sampling
There are several types of sampling methods in statistics. Each has its own use cases and advantages.
  • Simple Random Sampling: Every individual has an equal chance of being selected.
  • Systematic Sampling: Every nth individual is chosen from a list.
  • Stratified Sampling: The population is divided into subgroups (strata) and a random sample is taken from each stratum.
  • Cluster Sampling: The population is divided into clusters, and entire clusters are randomly selected.
  • Convenience Sampling: Samples are taken from a group that is conveniently accessible.

Our exercise uses cluster sampling, a method chosen due to its efficiency in handling groups (classes) within the college setting.
Statistical Sampling
Statistical sampling is a technique used to select a subset of individuals from a population to estimate characteristics of the whole population. The goal is to obtain a manageable number of observations that accurately represent the larger group.
Sampling methods can be classified broadly into two types: probability sampling and non-probability sampling. Probability sampling methods include simple random sampling, stratified sampling, and cluster sampling. Non-probability sampling includes techniques like convenience sampling and quota sampling.
In the exercise, statistical sampling is seen where the entire class (section) is surveyed. Though volunteers choose which class to survey, once chosen, every student in that class is included, fulfilling the criteria of cluster sampling within statistical sampling methods.
Education Statistics
Education statistics involve the collection and analysis of data related to educational institutions, processes, and outcomes. These statistics can help in making informed decisions about educational policies and practices.
Surveys are frequently used in educational statistics to gather opinions or feedback from students and faculty. The data collected can reflect the success of programs, areas needing improvement, and general satisfaction.
In our exercise, the administration collects opinions about course registration changes. This data is critical in assessing the efficacy of current procedures and identifying areas for enhancement. By using a structured method like cluster sampling, reliable data can be obtained, thereby supporting sound educational decisions.

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