Questions: Students in a high school woodworking class want to conduct a survey to determine the percentage of students in the school who are willing to pay a fee for participating in workshops. Students in each home room are alphabetically sorted by last name. A simple random sample of 12 home rooms was selected, and the survey was given to all 20 students in each home room. This plan is an example of which type of sampling? Cluster Stratified random Convenience Simple random Systematic

Students in a high school woodworking class want to conduct a survey to determine the percentage of students in the school who are willing to pay a fee for participating in workshops. Students in each home room are alphabetically sorted by last name. A simple random sample of 12 home rooms was selected, and the survey was given to all 20 students in each home room. This plan is an example of which type of sampling?
Cluster
Stratified random
Convenience
Simple random
Systematic

Transcript text: Students in a high school woodworking class want to conduct a survey to determine the percentage of students in the school who are willing to pay a fee for participating in workshops. Students in each home room are alphabetically sorted by last name. A simple random sample of 12 home rooms was selected, and the survey was given to all 20 students in each home room. This plan is an example of which type of sampling? Cluster Stratified random Convenience Simple random Systematic

Solution

Solution Steps

To determine the type of sampling method used in the given scenario, we need to analyze the process described. The students are grouped by home rooms, and a random sample of 12 home rooms is selected. Then, all students in those selected home rooms are surveyed. This method involves dividing the population into groups (home rooms) and then randomly selecting entire groups to survey.

Solution Approach

This is an example of Cluster Sampling because the population is divided into clusters (home rooms), and a random sample of clusters is chosen, with all members of the selected clusters being surveyed.

No Python code is needed for this theoretical question.### Step 1: Understand the Sampling Methods

To determine the type of sampling method used, we need to understand the definitions of each sampling method provided in the options:

Cluster Sampling: The population is divided into clusters, and a random sample of clusters is selected. All individuals within the selected clusters are surveyed.
Stratified Random Sampling: The population is divided into strata (groups) based on a characteristic, and a random sample is taken from each stratum.
Convenience Sampling: The sample is taken from a group that is conveniently accessible to the researcher.
Simple Random Sampling: Every individual in the population has an equal chance of being selected.
Systematic Sampling: Every nth individual is selected from a list of the population.

Step 2: Identify the Sampling Method Used

In the given question, the students selected a simple random sample of 12 home rooms and then surveyed all 20 students in each of those home rooms. This means that the population (all students in the school) was divided into clusters (home rooms), and a random sample of clusters (12 home rooms) was selected. All individuals within the selected clusters (all 20 students in each of the 12 home rooms) were surveyed.

Step 3: Match the Method to the Options

Based on the definitions and the sampling method used in the question, the method that matches is Cluster Sampling.