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Statistical Methods

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Statistics
School
The University of Utah
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Homework
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General Introduction
The Central Limit Theorem is one of the most fundamental and profound concepts in statistics.
According to theorem, any distribution with a well-defined mean and variance will have a
normally distributed sample mean if the size of the sample is sufficiently large. One of the
simplest and common examples to this is rolling a fair die. As the number of rolls increases, it
is more likely for the shape of the distribution of means to follow a normal distribution.
Objective
The purpose of this lab is to prove the central limit theorem by showing that the distribution of
sample mean follows a normal distribution as the number of samples ‘n’ increases.
Procedure and Statistical principle
The excel sheet contains the distribution of random numbers. Two sets of data with n=10 and
n=30 is taken for calculation. The average along each row is calculated and these sample means
are then plotted to study its distribution. The normality of the plots was checked using excel
functions after plotting the histogram of the corresponding data. The same calculation was then
carried out for the random distribution of n=30. It was experimentally seen that the distribution
of sample mean followed a normal distribution as the number of samples increased. A
representation of this theorem is shown below.

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Name and other details here. General Introduction The Central Limit Theorem is one of the most fundamental and profound concepts in statistics. According to theorem, any distribution with a well-defined mean and variance will have a normally distributed sample mean if the size of the sample is sufficiently large. One of the simplest and common examples to this is rolling a fair die. As the number of rolls increases, it is more likely for the shape of the distribution of means to follow a normal distribution. Objective The purpose of this lab is to prove the central limit theorem by showing that the distribution of sample mean follows a normal distribution as the number of samples ‘n’ increases. Procedure and Statistical principle The excel sheet contains the distribution of random numbers. Two sets of data with n=10 and n=30 is taken for calculation. The average along each row is calculated and these sample means are then plotted to study its distribution. The normality of the plots was checked using excel functions after plotting the histogram of the corresponding data. The same calculation was then carried out for the random distribution of n=30. It was experimentally seen that the distribution of sample mean followed a normal distribution as the number of samples increased. A representation of this theorem is shown below. Results and Discussion An exponentially distributed random numbers are considered for this experiment. This population of random numbers is then ...
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