Math Problem Statement
Analyze the sampling methods for systematic, random, and cluster sampling described in the provided scenarios. Determine which choice corresponds to each sampling type.
Solution
Here’s the analysis of the options in the image:
(a) Systematic Sample of Seats:
- Correct answer: "The supervisor takes a list of the seats and selects every 6th seat until 54 seats are selected."
- Reason: A systematic sample involves selecting every nth item from a list, ensuring a consistent interval throughout.
(b) Random Sample of Plants:
- Correct answer: "The botanist assigns each plant a different number. Using a random number table, he draws 72 of those numbers at random. Then, he selects the plants assigned to the drawn numbers."
- Reason: A random sample is characterized by giving every individual in the population an equal chance of being selected, which is achieved by random numbering and selection.
(c) Cluster Sample of Customers:
- Correct answer: "The analyst forms groups of 30 customers based on the cities the customers live in. Then, she selects all of the customers in 3 randomly chosen groups."
- Reason: A cluster sample involves dividing the population into groups (clusters), then randomly selecting entire groups for the sample.
Let me know if you'd like additional clarifications. Here are related questions to consider:
- How does systematic sampling differ from random sampling in ensuring representation?
- What are the key advantages of cluster sampling over simple random sampling?
- Why is the equal probability condition essential for random sampling?
- Can systematic sampling lead to biases? If so, in what scenarios?
- How do cluster and stratified sampling differ in terms of methodology?
Tip: When working with samples, always evaluate whether the sampling method aligns with the research question to ensure valid conclusions.
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Math Problem Analysis
Mathematical Concepts
Systematic Sampling
Random Sampling
Cluster Sampling
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12