Question

Suppose that we will take a random sample of size n from a population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean : (a) µ = 18, σ = 2, n = 22 (Round your answers of "σ " and "σ 2" to 4 decimal places.) (b) µ = 494, σ = .3, n = 125 (Round your answers of "σ " and "σ 2" to 4 decimal places.) (c) µ = 2, σ = .4, n = 9 (Round your answers of "σ " and "σ 2" to 4 decimal places.) (d) µ = 144, σ = 8, n = 1,159 (Round your answers of "σ " and "σ 2" to 4 decimal places.)

Answer #1

Suppose that we will take a random sample of size n
from a population having mean µ and standard deviation σ.
For each of the following situations, find the mean, variance, and
standard deviation of the sampling distribution of the sample
mean :
(a) µ = 20, σ = 2, n = 41
(Round your answers of "σ" and "σ2" to 4 decimal
places.)
µ
σ2
σ
(b) µ = 502, σ = .7, n = 132
(Round your answers of...

Suppose that we take a random sample of size n from a population
having a mean μ and a standard deviation of σ. What is the
probability or confidence we have that our sample will be within
+/- 1 of the population mean μ?
(a) μ = 10, σ = 2, n = 25

Suppose that we will randomly select a sample of 79 measurements
from a population having a mean equal to 21 and a standard
deviation equal to 8. (a) Describe the shape of the sampling
distribution of the sample mean . Do we need to make any
assumptions about the shape of the population? Why or why not?
Normally distributed ; yes , because the sample size is large . (b)
Find the mean and the standard deviation of the sampling...

A random sample of size n = 80 is taken from a
population with mean μ = -15.2 and standard deviation σ = 5.
What is the probability that the sample mean falls between -15
and -14? (Do not round intermediate calculations. If you
use the z table, round "z" values to 2 decimal
places. Round your final answer to 4 decimal places.

A random sample of size n = 50 is selected from a
binomial distribution with population proportion
p = 0.8.
Describe the approximate shape of the sampling distribution of
p̂.
Calculate the mean and standard deviation (or standard error) of
the sampling distribution of p̂. (Round your standard
deviation to four decimal places.)
mean =
standard deviation =
Find the probability that the sample proportion p̂ is
less than 0.9. (Round your answer to four decimal places.)

A random sample of size n = 241 is taken from a
population of size N = 5,588 with mean μ = −68
and variance σ2 = 183. [You may find it
useful to reference the z table.]
a-1. Is it necessary to apply the finite
population correction factor?
Yes
No
a-2. Calculate the expected value and the standard
error of the sample mean. (Negative values should be
indicated by a minus sign. Round "standard error" to 2
decimal places.)...

A random sample of size 64 is taken from a population with mean
µ = 17 and standard deviation σ = 16. What are the expected value
and the standard deviation for the sampling distribution of the
sample mean?

A random sample of size n = 49 is selected from a population
with mean μ = 54 and standard deviation σ = 14. What will be the
mean and standard deviation of the sampling distribution of x?

A random sample of size n = 186 is taken from a
population of size N = 5,613 with mean μ = −65
and variance σ2 = 183. [You may find it
useful to reference the z table.]
a-1. Is it necessary to apply the finite
population correction factor?
Yes
No
a-2. Calculate the expected value and the standard
error of the sample mean. (Negative values should be
indicated by a minus sign. Round "standard error" to 2
decimal places.)...

A random sample of size n = 40 is selected from a binomial
distribution with population proportion p = 0.25. (a) What will be
the approximate shape of the sampling distribution of p̂?
approximately normal skewed symmetric Correct: Your answer is
correct. (b) What will be the mean and standard deviation (or
standard error) of the sampling distribution of p̂? (Round your
answers to four decimal places.) mean 0.25 Correct: Your answer is
correct. standard deviation 0.0685 Correct: Your answer...

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