Math Problem Statement

True or False: The larger the sample size the closer the sampling distribution was to a normal distribution

Answer: Question 9

Solution

True.

This statement is based on the Central Limit Theorem (CLT), which asserts that as the sample size increases, the sampling distribution of the sample mean (or sum) approaches a normal distribution, regardless of the original distribution of the population. This convergence occurs as the sample size becomes large enough, typically n ≥ 30 is considered sufficiently large for the CLT to hold.

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Related Questions:

  1. What is the Central Limit Theorem and how does it work?
  2. How does sample size affect the standard error of the sample mean?
  3. What are the characteristics of a sampling distribution?
  4. How can we determine if a sample size is large enough for the CLT to apply?
  5. What happens to the shape of the sampling distribution when the sample size is small?

Tip: When using the Central Limit Theorem, always check if the sample size is sufficiently large (n ≥ 30), especially if the population distribution is not normal.

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Math Problem Analysis

Mathematical Concepts

Sampling Distribution
Central Limit Theorem
Probability Theory

Formulas

-

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 9-12