Question

True or False? Sample means will be closer to the population mean if the sample is large. True or False? Sample means never make mistakes. True or False? Sample means make mistakes that quantifiable and measured by the standard deviation of the sample mean. True or False? If a variable is distributed Normally, the sample means are Normally distributed, even if the sample is small. True or False? If a variable is NOT distributed Normally, the sample means are never Normally distributed. If a variable is NOT distributed Normally, the sample means can be Normally distributed if the sample is ____ (small / large). Explain what this means in English: If x has an average μ and a standard deviation σ, and if the sample is large, then the sample mean x ̅~N(μ,σ/√n) I have a population with an average μ and a standard deviation σ. I’m going to draw a sample from that population. If the sample is large enough, that is, if n is large enough, The average of sample averages is the ____ ____. The ____ ____ of sample averages is σ/√n The distribution of the sample averages follows a ______ distribution.

Answer #1

If a population is distributed with a mean μ and a standard
deviation σ, then the distribution of sample means is
distributed
A) normally with mean μ and standard deviation σ.
B) normally with mean μ and standard deviation σ/√(n).
C) with mean μ and standard deviation σ.
D) with mean μ and standard deviation σ/√(n).

A random sample is drawn from a normally distributed population
with mean μ = 25 and standard deviation σ =
1.5.
a. Are the sampling distributions of the sample
mean with n = 33 and n = 66 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 33 will have a normal
distribution.
No, only the sample mean...

A random sample is drawn from a population with mean μ = 72 and
standard deviation σ = 6.0. [You may find it useful to reference
the z table.]
a. Is the sampling distribution of the sample mean with n = 17
and n = 45 normally distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 17 will have...

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.

A random sample is drawn from a normally distributed population
with mean μ = 30 and standard deviation σ = 2.3.
[You may find it useful to reference the z
table.]
a. Are the sampling distribution of the sample
mean with n = 35 and n = 76 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 35...

A random sample is drawn from a population with mean μ
= 52 and standard deviation σ = 4.3.
a. Is the sampling distribution of the sample
mean with n = 13 and n = 39 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 13 will have a normal
distribution.
No, only the sample mean with n...

True or False?
1. σM equals the standard deviation
divided by the square root of the sample size
2. Larger samples more accurately reflect the population than
smaller samples
3. If n = 1, the standard error will equal the standard
deviation of the population
4. If a population is skewed, the distribution of sample means
will never be normal
5. The mean for the distribution of samples means is equal to
the mean of the population
6. As the sample...

A random sample is drawn from a population with mean μ
= 53 and standard deviation σ = 4.4. [You may find
it useful to reference the z table.]
a. Is the sampling distribution of the sample
mean with n = 13 and n = 38 normally
distributed?
Yes, both the sample means will have a normal distribution.
No, both the sample means will not have a normal
distribution.
No, only the sample mean with n = 13 will have...

1. For a population with a mean of μ = 55 and a standard
deviation of σ = 24, what is the standard error of the distribution
of sample means for a sample size of n=22?
2. If the population standard deviation is S= 17, how large a
sample is necessary to have a standard error that is less than 10
points?

A simple random sample of size n=40 is obtained from a
population with μ = 50 a n d σ = 4. Does the population
distribution need to be normally distributed for the sampling
distribution of x ¯ to be approximately normally distributed? Why
or why not? What is the mean and standard deviation of the sampling
distribution?

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