Question

When performing inference on population means we require that the data are normal and/or that the sample size is large (to use the Central Limit Theorem) so that the sample means have a sampling distribution that is at least approximately normal. The exact same statement (in bold) holds for performing inference on population variance(s) using the χ 2 or F-test.

(a) True

(b) False

Answer #1

TOPIC:Normal approximation for the test of variances.

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 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 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.

Hello, please review the statement below and determine if the
statement is right or not (and why).
Explain the central limit theorem
The central limit theorem states that when there’s a large
enough sample size (generally 30 or more) with a finite level of
variance, then the mean from all of the samples, from the same
population, will be approximately equal to the mean of the
population. There are three different components of the theorem.
The first is successive sampling...

Apply the Central Limit Theorem for Sample
Means
A population of values has a normal distribution with μ=77 and
σ=9.2. You intend to draw a random sample of size n=30.
Find the probability that a sample of size n=30n=30 is randomly
selected with a mean less than 76.8.
P(M < 76.8) =
Enter your answers as numbers accurate to 4 decimal places.
Answers obtained using exact z-scores or
z-scores rounded to 3 decimal places are accepted.

In a paired t-test, when will the distribution of sample means
of the differences be normal or approximately normal?
Select all that apply.
A.
When the sample is representative of the population of
interest
B.
When the sample size is at least 30
C.
When the distribution of differences in the population is
normal
D.
When all of the above are true

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.

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 ?

The central limit theorem (CLT) is a
statistical theory that states that given a sufficiently large
sample size from a population with a finite level of variance, the
mean of all samples from the same population will be approximately
equal to the mean of the population. (true or false?)

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