Question

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 sampling distribution looks more like the population
distribution as the sam- ple size increases.

can you please explain with example

Answer #1

Ans:

Correct options are:

For large random samples, the sampling distribution of is approximately normal, regardless of the shape of the population distribution.

The sampling distribution looks more like the population distribution as the sam- ple size increases.

e.g.

The population of adult males has a mean salary of $29,500 with a standard deviation of $2500. If a sample of 100 men is taken, what is the probability their mean salaries will be less than $29,000?

samplinf distribution of sample means(y-bar):

mean=29500

standard deviation=2500/sqrt(100)=250

z=(29000-29500)/250

z=-2

P(z<-2)=**0.0228**

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.

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

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...

Which of the following statements are TRUE?
Note that there may be more than one correct answer; select all
that are true.
1. a) All else being equal, the standard deviation of the
sampling distribution of the sample mean will be smaller for n = 10
than for n = 40.
b) The value of a statistic does not vary from sample to
sample.
c) Statistics have sampling distributions.
d) The value of a parameter does not vary from sample...

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...

Applying the Central Limit Theorem:
The amount of contaminants that are allowed in food products is
determined by the FDA (Food and Drug Administration). Common
contaminants in cow milk include feces, blood, hormones, and
antibiotics. Suppose you work for the FDA and are told that the
current amount of somatic cells (common name "pus") in 1 cc of cow
milk is currently 750,000 (note: this is the actual allowed amount
in the US!). You are also told the standard deviation...

(05.02 LC)
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? (4 points)
I. The distribution of the sample mean is exactly Normal.
II. The distribution of the sample mean is approximately
Normal.
III. The standard deviation is equal to that of the
population.
IV. The distribution of the population is exactly Normal.
a
I and...

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.

1)What does the Central Limit Theorem say, and why is it so
important to inferential statistics?
2) Why would someone want to know whether a sample had more than
30 observations?
3) What is the continuity correction?
4) What is a sampling distribution?
5) What are the basic distinctions between situations in which
the binomial, poisson, and hypergeometric distributions apply?
6) Suppose you have a population with mean ? and standard
deviation ?. What can you say about the sampling...

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