Question

summarize the implications of the central limit theorem

What is the most important application of it and why?

Answer #1

The central limit theorem tells us exactly what the shape of the distribution of means will be when we draw repeated samples from a given population. Specifically, as the sample sizes get larger, the distribution of means calculated from repeated sampling will approach normality.

Most useful Application of CLT is

CLT is important because under certain condition , we can approximate some distribution with Normal distribution although the distribution is not Normally distributed

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Describe the 2 methods used in the application of
Central Limit Theorem.

What is central limit theorem? What is the implication of
central limit theorem for estimation error?

What is wrong with the following statement of the central limit
theorem?
Central Limit Theorem. If the random variables X1,
X2, X3, …, Xn are a random sample of size n from any distribution
with finite mean μ and variance σ2, then the distribution of will
be approximately normal, with a standard deviation of σ / √n.

Question Central Limit Theorem
a)According to the Central Limit Theorem, what
are the mean and standard deviation of the sampling distribution of
sample means?
b)A population has a mean ?=1800 and a standard
deviation ?=40. Find the mean and standard deviation of the
sampling distribution of sample means when the sample size
n=100.

Why is the Central Limit Theorem considered to be so important
for inferential statistics? Consider the mean, standard error, and
shape of the sampling distribution of the means in your answer.
Also describe the role played, if any, by the underlying or
population distribution, sample distribution, and sampling
distribution.

What is the central limit theorem? What are some of the
properties of distribution mean when the central limit theorem is
in effect?

Describe the Central Limit Theorem.

Explain the central limit theorem. Describe an experiment that
could be used to verify the central limit theorem.

Review: Central Limit Theorem
1 point possible (graded)
The Central Limit Theorem states that if
X1,…,Xn are i.i.d. and
E[X1]=μ<∞
;
Var(X1)=σ2<∞,
then
n−−√[(1n∑i=1nXi)−μ]−→−−n→∞(d)Wwhere W∼N(0,?).
What is Var(W)? (Express your answer in terms of n, μ and
σ).

Write a paragraph or more to explain what the central limit
theorem is and what it is used for in statistics?

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