Question

When we can consider the Sampling distribution of the sample means as a Normal distribution?

Choose 1 response :

a. If the population is Normally distributed

b. If there is no information about population distribution and
sample size is 24

c. If the population is not Normally distributed and sample size is
24

d. If population is not Normally distributed but sample size
n≥30

Answer #1

Can a normal approximation be used for a sampling distribution
of sample means from a population with μ=43 and σ=8, when
n=36?
Answer
TablesKeypad
Yes, because the mean is greater than 30.
No, because the sample size is more than 30.
Yes, because the sample size is at least 30.
No, because the standard deviation is too small.

If a population is normally distributed, the distribution of the
sample means for a given sample size n will
A. be positively skewed
B. be negatively skewed
C. be uniform
D. be normal
E. none of the above
If a population is not normally distributed, the distribution of
the sample means for a given sample size n will
A. take the same shape as the population
B. approach a normal distribution as n increases
C. be positively...

Can a normal approximation be used for a sampling distribution
of sample means from a population with μ=53 μ=53 and σ=9 σ=9 , when
n=64 n=64 ?

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

Determine whether the hypothesis test involves a sampling
distribution of means that is a normal distribution, Student t
distribution, or neither. Claim: ? = 119. Sample data: ? = 15, ?̅ =
103, ? = 15.2. The sample data, for this simple random sample,
appear to come from a normally distributed population with unknown
? and ?.

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

1) Determine whether the following hypothesis test involves a
sampling distribution of means that is a normal distribution,
Student t distribution, or neither.
Claim about IQ scores of statistics instructors: μ > 100.
Sample data: n = 15, x ¯= 118, s = 11.
The sample data appear to come from a normally distributed
population with unknown μand σ.
a) student T-distribution
b) Normal distribution
c) Neither
2)
Determine whether the following hypothesis test involves a
sampling distribution of means...

True or False?
The sampling distribution of the sample mean of a non-normally
distributed population will also be normally distributed as long as
the sample size is greater than 10.
The sampling distribution of the sample mean of a normally
distributed population will not be normally distributed if sample
size is less than 30.

Question 2: Which of the following statements about the
sampling distribution of means is not true?
A. A sample distribution's mean will always equal the parent
population distribution's mean
B. The sampling distribution of means approximates the normal
curve.
C. The mean of a sampling distribution of means is equal to the
population mean.
D. The standard deviation of a sampling distribution of means is
smaller than the standard deviation of the population.

In which of the following scenarios can we assume a Normal
distribution for the sample mean? a. Sample of size 2 comes from a
population with normal distribution (known variance) b. Sample of
size 10 comes from a population with normal distribution (unknown
variance) c. Sample of size 300 comes from a population with some
unknown distribution d. Sample of size 15 comes from a population
with some unknown distribution

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