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:
- What is the Central Limit Theorem and how does it work?
- How does sample size affect the standard error of the sample mean?
- What are the characteristics of a sampling distribution?
- How can we determine if a sample size is large enough for the CLT to apply?
- 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
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