Question

**a.** What is the standard error of a sampling
distribution? (out of the following)

the mean, the probability, the bias, the standard deviation, or the variance

**b.** What is the standard deviation of a sampling
distribution called? (out of the following)

the spread, the variance, the standard error, the mean, the standard variance

**c.** List two unbiased estimators and their
corresponding parameters. (Select all that apply out of the
following.)

μ is an unbiased estimator for x-bar, *p* is an unbiased
estimator for p̂, p̂ is an unbiased estimator for *p,* σ is
an unbiased estimator for σ_{x-bar,} x-bar is an unbiased
estimator for μ, σ_{x-bar} is an unbiased estimator for
σ

**d.** Describe how the variability of the
distribution changes as the sample size increases. (out of the
following)

As the sample size increases, the variability decreases.--It cannot be determined.--- As the sample size increases, the variability stays the same.----As the sample size increases, the variability increases.

**e.** Suppose *x* has a distribution with
*μ* = 59 and *σ* = 14.

**1)** If random samples of size *n* = 16
are selected, can we say anything about the x-bar distribution of
sample means? (out of the following)

Yes, the x-bar distribution is normal with mean μ
_{x-bar} = 59 and σ _{x-bar} = 0.9.------Yes, the x
distribution is normal with mean μ _{x-bar} = 59 and σ
_{x-bar} = 14.--------Yes, the x-bar distribution is normal
with mean μ _{x-bar} = 59 and σ _{x-bar} =
3.5.-----No, the sample size is too small.

**2)** If the original *x* distribution is
*normal*, can we say anything about the x-bar distribution
of random samples of size 16? (out of the following)

Yes, the x-bar distribution is normal with mean μ
_{x-bar} = 59 and σ _{x-bar} = 0.9.--------Yes, the
x-bar distribution is normal with mean μ _{x-bar} = 59 and
σ _{x-bar} = 14.-------No, the sample size is too
small.-------Yes, the x-bar distribution is normal with mean μ
_{x-bar} = 59 and σ _{x-bar} = 3.5.

**3)** Find *P*(55 ≤ *x* ≤ 60).
(Round your answer to four decimal places.)

Answer #1

1. Accrotime is a manufacturer of quartz crystal watches.
Accrotime researchers have shown that the watches have an average
life of 29 months before certain electronic components deteriorate,
causing the watch to become unreliable. The standard deviation of
watch lifetimes is 5 months, and the distribution of lifetimes is
normal.
(a) If Accrotime guarantees a full refund on any defective watch
for 2 years after purchase, what percentage of total production
will the company expect to replace? (Round your answer...

Suppose x has a distribution with μ = 75 and
σ = 8.
(a) If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
No, the sample size is too small.Yes, the x
distribution is normal with mean μx =
75 and σx =
0.5. Yes, the x distribution is
normal with mean μx = 75 and
σx = 2.Yes, the x
distribution is normal with mean μx =
75...

Suppose x has a distribution with μ = 25 and
σ = 2.
(a) If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
Yes, the x distribution is normal with mean
μx = 25 and
σx = 0.5.No, the sample size is too
small. Yes, the x
distribution is normal with mean μx =
25 and σx = 2.Yes, the x
distribution is normal with mean μx =
25...

6.5-4) Suppose x has a distribution with μ =
39 and σ = 20.
(a)If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
Yes, the x distribution is normal with mean
μx = 39 and
σx = 5.
No, the sample size is too small.
Yes, the x distribution is normal with mean
μx = 39 and
σx = 1.3.
Yes, the x distribution is normal with mean...

Updated - exactly how it is asked
Suppose x has a distribution with μ = 59 and
σ = 8.
If the original x distribution is normal, can
we say anything about the x distribution of random samples of size
16?
Yes, the x distribution is normal with mean μ x = 59
and σ x = 0.5.Yes, the x distribution is normal with
mean μ x = 59 and σ x = Yes, the x
distribution is normal with...

Suppose x has a distribution with μ = 22 and
σ = 20.
(a) If random samples of size n = 16 are selected, can
we say anything about the x distribution of sample
means?
Yes, the x distribution is normal with mean μ x = 22
and σ x = 1.3
No, the sample size is too small.
Yes, the x distribution is normal with mean μ x = 22
and σ x = 5
Yes, the x distribution...

Suppose x has a normal distribution with mean μ = 45 and
standard deviation σ = 10.
Describe the distribution of x values for sample size n = 4.
(Round σx to two decimal places.)
μx =
σx =
Describe the distribution of x values for sample size n = 16.
(Round σx to two decimal places.)
μx =
σx =
Describe the distribution of x values for sample size n = 100.
(Round σx to two decimal places.)
μx...

1. A sampling distribution of the mean has a
mean μ X̄ =45 μ X̄ =45 and a
standard error σ X̄ =7 σ X̄ =7
based on a random sample of n=15.n=15.
a. What is the population mean?
b. What is the population standard
deviation?
Round to two decimal places if necessary
2. If it is appropriate to do so, use the normal approximation
to the p^ p^ -distribution to calculate the
indicated probability:
Standard Normal Distribution Table
n=80,p=0.715n=80,p=0.715
P( p̂ > 0.75)P( p̂ > 0.75) =
Enter 0...

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...

Suppose x has a normal distribution with mean μ = 16 and
standard deviation σ = 11. Describe the distribution of x values
for sample size n = 4. (Round σx to two decimal places.)
μx = σx = Describe the distribution of x values for sample size
n = 16. (Round σx to two decimal places.)
μx = σx = Describe the distribution of x values for sample size
n = 100. (Round σx to two decimal places.)
μx...

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