Math Problem Statement

A study is conducted to understand the average height of adult residents in a city. The sample is drawn from people attending a basketball tournament in that city. Which of the following best describes the bias introduced in this sampling method? (a) Voluntary Response Bias (b) Nonresponse Bias (c) Undercoverage Bias (d) Convenience Sampling Bias (e) None of the above.

Solution

The question concerns the type of bias introduced in a study that determines the average height of adults in a city using a sample of individuals attending a basketball tournament.

The correct answer is (c) Undercoverage Bias. Here's why:

  • People attending a basketball tournament are likely to be taller than the average adult in the city due to the nature of the sport and its fan base, which often includes players and enthusiasts. This leads to an underrepresentation of shorter individuals in the sample.
  • This is a form of selection bias but is more specifically categorized as undercoverage, as the sampling method systematically excludes certain parts of the population.

If you think it should be selection bias (as written in your annotation), note that selection bias is a broader term. Undercoverage bias is a more specific subset of selection bias.

Would you like a detailed explanation of the different types of biases listed?

Here are 5 follow-up questions to deepen understanding:

  1. What distinguishes undercoverage bias from convenience sampling bias?
  2. How would voluntary response bias affect this type of study?
  3. Can you describe a way to minimize bias in sampling for this scenario?
  4. How is the concept of selection bias broader than undercoverage bias?
  5. Why is it important to identify and mitigate bias in sampling methods?

Tip:

Always ensure the sampling frame represents the entire population of interest to minimize biases!

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Math Problem Analysis

Mathematical Concepts

Statistics
Sampling Methods
Bias in Sampling

Formulas

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Theorems

Bias Classification in Statistical Sampling

Suitable Grade Level

Grades 10-12