Problem 19 - BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Question

The staff of a student newsletter wants to conduct a survey of the students' favorite television shows. There are 1225 students in the school. Describe a method for selecting a random sample of 250 students to survey.

Step-by-Step Solution

Answer

Assign each student a unique number, and use a random number generator to select 250 numbers. The students with these assigned numbers would make up the random sample for the survey.

Step 1: Understand the Problem

The main problem in this exercise is the selection of a random sample of 250 students from a population of 1225 students, in order to conduct a survey of their favorite TV shows. We can do this using a number of different sampling methods.

Step 2: Decide the Method of Random Selection

For this size population, and to ensure fair and random selection, a simple random sample is most appropriate. This could be done using a random number generator or drawing names from a hat. Each student in the school would be equally likely to be chosen, ensuring that our sample is representative.

Step 3: Implement the Selected Method

Let's use a random number generator as an example. Assign a unique number to each of the 1225 students, perhaps according to their roll call number or student ID. Use a random number generator to select 250 numbers from this range. The students associated with these numbers would be included in the sample.

Key Concepts

survey methodology

Survey methodology is the science behind how a survey is conducted. It includes all the steps that go into collecting, analyzing, and interpreting data from a subset of a population to draw conclusions about the entire group.
One crucial part of survey methodology is selecting a sample. This process ensures that the results will be accurate and reflective of the larger population. Here are some key points to consider:

• Sample Size: The number of respondents chosen for the survey. It needs to be large enough to provide reliable results. In our case, 250 students out of 1225 is a good size.
• Sampling Method: This refers to how participants are selected. It must be unbiased and fair to represent the population well.
• Data Collection: Gathering information through methods such as interviews, surveys, or questionnaires.

Each of these components needs careful planning and execution to ensure accurate survey results. Survey methodology helps reduce errors and biases, which allows for more reliable conclusions.

simple random sample

A simple random sample is a fundamental sampling technique where every individual of a population has an equal chance of being selected. This method is straightforward and unbiased, making it one of the best ways to obtain a genuine representation of a population.
When using a simple random sample, each member of the population is assigned a number or identifier. Using a tool like a random number generator, a predetermined number of identifiers (or people) are selected to make up the sample.
Some advantages of this method include:

• Equality: Every member has the same chance of selection, eliminating selection bias.
• Simplicity: It is easy to implement and does not require complex procedures.
• Reliability: Provides a strong basis for statistical inference.

Considerations must be taken when ensuring that the list of the population is complete and accurate. Simple random sampling forms a robust foundation for any well-conducted survey.

student survey design

Designing a student survey involves thoughtful planning to gather meaningful and reliable data. It means creating a survey that is clear, concise, and tailored to the audience's understanding.
Here are important factors when designing a student survey:

• Purpose: Understand the primary goal of the survey. Is it to find out TV preferences, study habits, or something else?
• Questions: Craft questions that are easy to understand and directly related to the survey's purpose. They should aim to avoid bias and complexity.
• Distribution: Choose a method to distribute the survey, like online forms, in-person interviews, or paper questionnaires.
• Confidentiality: Ensure students' responses are kept private to encourage honest and accurate answers.

A well-designed student survey not only provides insights but also respects the respondents' time and privacy, all the while ensuring the results are reflective of the larger student body.