Question

The Central Limit Theorem suggests that as the sample size increases the distribution of the sample averages approaches a normal distribution, regardless of the nature of the distribution of the variable itself.

true or false

Answer #1

The Central Limit Theorem suggests that as the sample size increases the distribution of the sample averages approaches a normal distribution, regardless of the nature of the distribution of the variable itself. That is-

If X follows a distribution with mean and standard deviation , and x1, x2, x3 ,................xn be the random sample from X then the distribution of sample mean x bar follows Normal distribution with mean and standard deviation / sqrt(n)

Hence **This is TRUE.**

**Hope this will help you. Thank you
:)**

True or False.
The central limit theorem states that as the number of sample
size increases, the distribution of the sample means approximates
to a normal distribution.

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...

a) What is the Central Limit Theorem? It is always true
that as the sample size, n, increases, the distribution of the
sample means will be approximately normally distributed.
Explain
b) If the underlying population of study is not normally
distributed, how large should the sample size be? What if the
population is normally distributed ?

Which one of the following statements is
true?
A. The Central Limit Theorem states that the sampling
distribution of the sample mean, y , is approximately
Normal for large n only if the distribution of the population is
normal.
B. The Central Limit Theorem states that the sampling
distribution of the sample mean, y , is approximately
Normal for small n only if the distribution of the population is
normal.
C. The Central Limit Theorem states that the sampling
distribution...

The Central Limit Theorem indicates that in selecting random
samples from a population, the sampling distribution of the the
sample mean x-bar can be approximated by a normal distribution as
the sample size becomes large.
Select one: True False

The Central Limit Theorem says that when sample size n is taken
from any population with mean μ and standard deviation σ when n is
large, which of the following statements are true?
The distribution of the sample mean is approximately
Normal.
The standard deviation is equal to that of the population.
The distribution of the population is exactly Normal.
The distribution is biased.

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.

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 ?

Which of the following is NOT a conclusion of the Central Limit
Theorem? Choose the correct answer below.
A. The distribution of the sample means x overbar will, as the
sample size increases, approach a normal distribution.
B. The mean of all sample means is the population mean mu.
C. The distribution of the sample data will approach a normal
distribution as the sample size increases.
D. The standard deviation of all sample means is the population
standard deviation divided...

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

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