scholarly journals Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

2006 ◽  
Vol 14 (3) ◽  
Author(s):  
M. Leigh Lunsford ◽  
Ginger Holmes Rowell ◽  
Tracy Goodson-Espy
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Student Understanding ◽  
Classroom Research ◽  
Research Assessment ◽  
The Central Limit Theorem ◽  
Sampling Distributions ◽  
Probability And Statistics

scholarly journals Understanding the Central Limit Theorem the Easy Way: A Simulation Experiment

Proceedings ◽  
2018 ◽  
Vol 2 (21) ◽  
pp. 1322
Author(s):  
Monica E. Brussolo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Electronic Device ◽  
Probability Distributions ◽  
Online Simulation ◽  
The Central Limit Theorem ◽  
Sampling Distributions ◽  
Initial Stage ◽  
Random Samples

Using a simulation approach, and with collaboration among peers, this paper is intended to improve the understanding of sampling distributions (SD) and the Central Limit Theorem (CLT) as the main concepts behind inferential statistics. By demonstrating with a hands-on approach how a simulated sampling distribution performs when the data used has different probability distributions, we expect to clarify the notion of the Central Limit Theorem, and the use of samples in the hypothesis testing process for populations. This paper will discuss an initial stage to create random samples from a given population (using Excel) with collaboration of the students, which has been tested in the classroom. Then, based on that experience, a second stage in which we created an online simulation, controlled by the professor, and in which the students will participate during class time using an electronic device connected to internet. Students will create simple random samples from a variety of probability distributions simulated online in a collaborative way. Once the samples are generated, the instructor will combine and summarize the resulting sample statistics using histograms and the results will be discussed with the students. The objective is to teach some of the central topics of introductory statistics, the Central Limit Theorem and sampling distributions with an interactive and engaging approach.

Demonstrating the Central Limit Theorem

1986 ◽  
Vol 13 (3) ◽  
pp. 155-156 ◽  
Author(s):  
David E. Johnson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
The Central Limit Theorem ◽  
Sampling Distributions ◽  
Beginning Students

Explaining abstract, theoretical distributions to beginning students is sometimes difficult. This article describes a demonstration that helps to make the central limit theorem for generating sampling distributions concrete and understandable.

Technology Tips: Teaching Sampling Distributions Using Autograph

2011 ◽  
Vol 105 (3) ◽  
pp. 226-229 ◽  
Author(s):  
James R. Kett
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
The Central Limit Theorem ◽  
Sampling Distributions ◽  
Software Program

The author uses Autograph, a powerful software program, to illustrate sampling distributions and to demonstrate the central limit theorem.

Assessment of student understanding of the central limit theorem

CHANCE ◽  
2008 ◽  
Vol 21 (1) ◽  
pp. 27-32
Author(s):  
M. Leigh Lunsford ◽  
Ginger Holmes Rowell ◽  
Tracy Goodson-Espy
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Student Understanding ◽  
The Central Limit Theorem

Assessment of Student Understanding of the Central Limit Theorem

CHANCE ◽  
2008 ◽  
Vol 21 (1) ◽  
pp. 27-32
Author(s):  
M. Leigh Lunsford ◽  
Ginger Holmes Rowell ◽  
Tracy Goodson-Espy
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Student Understanding ◽  
The Central Limit Theorem

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

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