Question

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

Answer #1

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.

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.

Please explain the following:
(a) What is a sampling distribution?
(b) Central Limit Theorem.

What is sampling distribution? What is Central Limit
Theorem? What can we gain from this type of statistical
information?

The central limit theorem (CLT) predicts that sampling from a
normally distributed population results in a normally distributed
SDM. What would the shape of the SDM be if the population is
Skewed? Why?

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.

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

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...

The Central Limit Theorem implies that [Select the correct
answers - There may be more than one correct answer. Negative
marking will apply for incorrect selections.]
(a) All variables have bell-shaped sample data distributions
if a random sample con- tains at least about 30 observations.
(b) Population distributions are normal whenever the
population size is large.
(c) For large random samples, the sampling distribution of y ̄
is approximately normal, regardless of the shape of the population
distribution.
(d) The...

For Central Limite Theorem, if n>30, we say the sampling
distribution is normal. However, most of the time, with population
standard deviation unknown, we still have to use t value to compute
a confidence interval. But I wonder for normal distribution(z
distribution), even though we do not know population sd, why cannot
we use z value directly to compute confidence interval, as it has
stated in central limit theorem that the distribution is
normal.

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