Question

**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.

Answer #1

Solution :

(a)

According to the Central Limit Theorem, what are the mean and standard

deviation of the sampling distribution of sample means are,

_{}
= and
_{}

(b)

Given that,

mean = = 1800

standard deviation = = 40

n = 100

The sampling distribution of mean and standard deviation is ,

_{}
= 1800 and

_{}
=
/
n = 400 /
100 = 400 / 10 = 40

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.

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...

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?

Given a population with mean μ=100 and variance
σ2=81, the Central Limit Theorem applies
when the sample size n≥30. A random sample of size
n=30 is obtained.
What are the mean, the variance, and the standard deviation of
the sampling distribution for the sample mean?
Describe the probability distribution of the sample mean and
draw the graph of this probability distribution with its mean and
standard deviation.
What is the probability that x<101.5?
What is the probability that x>102?
What...

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

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 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...

True or False:
___________ According to the Central Limit Theorem, the sampling
distribution of means approximates a normal distribution given
sample sizes greater than 30.
___________ According to the textbook, single sample t-tests are
used instead of single sample z-tests when the population standard
deviation (σ) is unknown.
___________ A set of events is said to be mutually exclusive
when it contains all possible outcomes.
___________ Two-tailed tests predict the direction of the
effect

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...

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