Question

The Central Limit Theorem allows us to make predictions about where a sample mean will fall in a distribution of sample means. One way it does this is by explaining (using a formula) how the shape of the distribution will change depending on the sample size. What part of the Central Limit Theorem tells us about the shape of the distribution?

The part that explains that there is no standardized table you can use to find probabilities once you use samples larger than

There is no part in the Central Limit Theorem that describes the shape of the distribution of sample means

The part that explains that Standard Error is a function of the population standard deviation divided by the square root of the sample size

The part that explains that the estimated mean of the sampling distribution will be the same as the population mean

Answer #1

**Solution:**

The Central Limit Theorem allows us to make predictions about where a sample mean will fall in the distribution of sample means. One way it does this is by explaining (using a formula) how the shape of the distribution will change depending on the sample size. What part of the Central Limit Theorem tells us about the shape of the distribution?

**Answer: The part that explains that Standard Error is a
function of the population standard deviation divided by the square
root of the sample size.**

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 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...

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...

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.

1. The Central Limit Theorem
A. States that the OLS estimator is BLUE
B. states that the mean of the sampling distribution of the
mean is equal to the population mean
C. none of these
D. states that the mean of the sampling distribution of the
mean is equal to the population standard deviation divided by the
square root of the sample size
2. Consider the regression equation Ci= β0+β1 Yi+ ui where C is
consumption and Y is disposable...

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

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.

The Central Limit Theorem is used when dealing with: mean from a
sample, individual data point ,chi-squared distributions, or
sampling distribution of a standard deviation? When using the CLT,
we use σ √ n for the: standard deviation for individual values,
mean for the sample, standard deviation of the sample means, or
sample size?

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 ?

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