Math Problem Statement

Employees at a website want to select a sample of their users to ask for a donation. They randomly select one of the first [25] users each day and show them a message asking for a donation. They also show the message to every [25^\text{th}] user from that point on. What type of sample is this? Choose 1 answer: Choose 1 answer: (Choice A) Simple random sample A Simple random sample (Choice B) Stratified random sample B Stratified random sample (Choice C) Cluster random sample C Cluster random sample (Choice D) Systematic random sample D Systematic random sample (Choice E) None of the above E None of the above

Solution

The correct answer is:

(Choice D) Systematic random sample.

Explanation:

  • Systematic sampling involves selecting every kthk^\text{th} individual from a population after a randomly chosen starting point. In this case:
    • A random start is chosen (one of the first 25 users).
    • From that point on, every 25th user is selected for the donation message.

This process perfectly matches the definition of a systematic random sample.

Would you like further clarification on systematic sampling?


Related Questions:

  1. What is the difference between systematic sampling and simple random sampling?
  2. How does stratified sampling work, and when is it used?
  3. Can systematic sampling introduce bias? Why or why not?
  4. What is an example of a real-world application of cluster sampling?
  5. How does randomization improve the accuracy of sampling?

Tip: In systematic sampling, make sure the interval kk is appropriate to avoid patterns that might bias the sample.

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Math Problem Analysis

Mathematical Concepts

Sampling Methods
Systematic Sampling

Formulas

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Theorems

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Suitable Grade Level

Grades 10-12