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

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 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 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?
17 and 2, respectively.
17 and 64, respectively.
17 and 16, respectively.
17 and 1, respectively.

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?
17 and 2, respectively.
17 and 64, respectively.
17 and 16, respectively.
17 and 1, respectively.

A random sample is selected from a population with mean
μ = 102 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 = 12
μ =
σ =
(b) n = 13
μ =
σ =
(c) n = 37
μ =
σ =
(d) n = 70
μ =
σ =
(f) n = 140...

A random sample of size n = 52 is taken from a finite population
of size N = 515 with mean μ = 253 and variance σ2 = 398. [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.(Round “expected value” to a whole number and "standard error"
to 4 decimal places.)

Suppose a random sample of n = 16 observations is selected from
a population that is normally distributed with mean equal to 102
and standard deviation equal to 10.
a) Give the mean and the standard deviation of the sampling
distribution of the sample mean x.
mean =
standard deviation =
b) Find the probability that x exceeds 106. (Round your
answer to four decimal places.)
c) Find the probability that the sample mean deviates from the
population mean μ...

A random sample of size n = 101 is taken from a
population of size N = 2,719 with a population proportion
of p = 0.67. [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 proportion. (Round "expected
value" to 2 decimal places and "standard error" to 4 decimal
places.)
b. What is the...

A random sample is drawn from a population having σ = 15.
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...

Suppose a random sample of n = 25 observations is
selected from a population that is normally distributed with mean
equal to 108 and standard deviation equal to 14.
(a) Give the mean and the standard deviation of the sampling
distribution of the sample mean
x.
mean
standard deviation
(b) Find the probability that
x
exceeds 113. (Round your answer to four decimal places.)
(c) Find the probability that the sample mean deviates from the
population mean ? = 108...

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