Business Analysis: The Central Limit Theorem and Sampling Methods

This essay provides a detailed explanation of the central limit theorem and its significance in business analysis. It emphasizes the theorem's role in understanding sampling distributions, hypothesis testing, and the behavior of simulation models. The essay highlights how the central limit theorem allows researchers to draw meaningful conclusions from samples, especially due to its indication of repeated distribution across samples and its ability to predict the shape of distribution graphs. It also touches on the impact of sample size on standard deviation and normality. The document concludes by referencing relevant academic papers.

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Central limit theorem is the most used theorem which provides the best fundamental
results in statistics. In central limit theorem, the standard deviation and population mean
indicates distribution is repeated in across samples when the mean the population is equal (Alaya
& K, 2014). The central limit theory tells clearly what is meant by the shape of distribution when
repeated samples are drawn from a certain populations. It allows researchers to understand better
sampling which is crossed repeated thus concluding the given results from samples which is
important to the organization.
Central limit helps the researchers when testing hypothesis about the samples mostly
because it starts and uses the sampling distribution. The sampling distribution represents the
estimated distributions in repeated samples (Feller, 2015). When they are tested, the sample mean
or something bigger is small in sufficient ways making the rejection of assertion sample to be
similar to the general public.
When the size of the sample increases, the standard deviation decreases and when the
size of the sample decreases the sample standard deviation increases. The shape of the graph in
distribution which means the repeated samples will be drawn from that given population. This is
because as the size of population gets larger, the calculated distribution means that it will be a
repeated sampling approach which will show normality (Alaya & K, 2014). This is what makes the
theorem to be remarkable when the results hold the shape of the distribution graph of the original
population.
In simulation model, the behavior of the sample model is done by running some
simulation. In every trial, the numerical value input the variances thus the model is used in
evaluation of the interest outcomes and collecting the values for analysis (Feller, 2015).

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References
Alaya, M. B., & K, A. (2014). Central limit for the multilevel Monte Carlo Euler method. The
Annals of Applied Probability, 211-234.
Feller, W. (2015). Generalisation of a probability limit theorem of Cramerin selected papers.
Spring Cham, 601-612.