Question

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

Answer #1

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.

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).

Which of the following statements is not consistent with
the Central Limit Theorem?
1. The Central Limit Theorem applies to non-normal population
distributions.
2. The standard deviation of the sampling distribution will be
equal to the population standard deviation.
3. The sampling distribution will be approximately normal when
the sample size is sufficiently large.
4. The mean of the sampling distribution will be equal to the
population mean.

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 relationship among sampling distributions, the Central
limit Theorem and interval estimation ?

1. The Central Limit Theorem tells us that as the sample size
increases, the center of the sampling distribution of x ̅
____________.
a. increases
b. decreases
c. stays the same
2. The Central Limit Theorem tells us that as the sample size
increase, the spread of the sampling distribution of x ̅
____________.
a. increases
b. decreases
c. stays the same
3. What is the best way we know to generate data that give a
fair and accurate picture...

According to the central limit theorem, a sample mean distribution
is aproximately a normal distribution , what are the mean and
standard deviation of this normal distribution ?

According to the central limit theorem, if a sample of size 81
is drawn from a population with a variance of 16, the standard
deviation of the distribution of the sample means would equal
_______.
.98
.44
.68
.87
.75

According to the Central Limit Theorem, The traditional sample
size that separates a large sample size from a small sample size is
one that is greater than

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 37 seconds ago

asked 4 minutes ago

asked 6 minutes ago

asked 6 minutes ago

asked 6 minutes ago

asked 6 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 9 minutes ago

asked 13 minutes ago

asked 13 minutes ago