Question

**1. Suppose a random sample of 100 elements is selected
from a non-normally distributed
population with a mean of µ = 30 and a standard deviation of σ =
8.
a. What is the expected value of ?̅?
b. What is the standard error of the mean ??̅?
c. What is the sampling distribution of ?̅? Describe its
properties.
d. If we select a random sample of size n = 100, what is the
probability that ?̅will fall
within ± 1 of µ= 30? That is, what is P(29 ≤ ?̅≤ 31)?
e. If the population size is N = 10,000, what is the standard error
of the mean ??̅?
f. If the population size is N = 2,000, what is the standard error
of the mean ??̅?**

Answer #1

A random sample of size n has been selected from a normally
distributed population whose standard deviation is σ. In hypothesis
testing for the population mean, the t-test should be used instead
of the z-test if: A. n>30 and σ is unknown B. n<30 and σ is
known C. both A and B are true D. both A and B are false

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 selected from a population with mean μ = 100
and standard deviation σ = 10.
Determine the mean and standard deviation of the x sampling
distribution for each of the following sample sizes. (Round the
answers to three decimal places.)
(a) n = 8 μ = σ =
(b) n = 14 μ = σ =
(c) n = 34 μ = σ =
(d) n = 55 μ = σ =
(f) n = 110...

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a. If the sample size is n = 30 and the sample mean x = 100,
what is the 95% confidence interval estimate of the population mean
µ?
b. If the sample size is n = 120 and the sample mean x = 100,
what is the 95% confidence interval estimate of the population mean
µ?
c. If the sample size is n = 480 and the sample...

A simple random sample of size n is drawn from a population that
is normally distributed. The sample mean, x overbar, is found to
be 110, and the sample standard deviation, s, is found to be
10.
(a) Construct an 80% confidence interval about mu if the
sample size, n, is 29.
(b) Construct an 80% confidence interval about mu if the
sample size, n, is 21.
(c) Construct a 70% confidence interval about mu if the
sample size, n,...

A simple random sample of size 11 is drawn from a normal
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¯x=26.8.
a.) Construct a 85% confidence level for μ. (Round answers to two
decimal place.)
margin of error:
lower limit:
upper limit:
b.) If the population were not normally distributed, what
conditions would need to be met? (Select all that apply.)
the population needs to be uniformly distributed
σ is unknown
simple random sample
large enough sample size...

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distribution?

A simple random sample of size n is drawn from a population that
is normally distributed. The sample mean, x overbar, is found to
be 109, and the sample standard deviation, s, is found to be 10.
(a) Construct a 96% confidence interval about mu if the sample
size, n, is 13.
(b) Construct a 96% confidence interval about mu if the sample
size, n, is 29.
(c) Construct a 99% confidence interval about mu if the...

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
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No, only the sample mean with n = 35...

A random variable X is normally distributed. It has a mean of
254 and a standard deviation of 21.
List the givens with correct symbols:
? (σ N X̄ μ s X p n) = 254
? (X̄ n σ s X p μ N) = 21
a) If you take a sample of size 21, can you say what the shape of
the sampling distribution for the sample mean is?
? Yes No
Why or why not? Check all...

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