Question

Suppose x^{+}_{r }denotes the
sample mean in a sample of size r,
and

assume:

x^{+}_{r} ~ N(
µ = 350, σ^{2} /
r).

(i)
If r < s, what is
the
efficieny of x^{+}_{r} relative
to x^{+}_{s} ?

(ii) Consider the pooled mean obtained by mixing two samples of size r

and size s. What
is the efficiency of the pooled mean relative
to x^{+}_{r} ?

Answer #1

Suppose x+r denotes the
sample mean in a sample of size r,
and
assume:
x+r ~ N(
µ = 350, σ2 /
r).
If r < s, what
is the
efficieny of x+r relative
to x+s ?
Consider the pooled mean obtained by mixing two
samples of size r
and size s. What is the efficiency
of the pooled mean relative to x+r
?

Let X be the mean of a random sample of size n from a N(θ, σ2)
distribution,
−∞ < θ < ∞, σ2 > 0. Assume that σ2 is known. Show that
X
2 − σ2
n is an
unbiased estimator of θ2 and find its efficiency.

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...

R Simulation:
For n = 10, simulate a random sample of size n from N(µ,σ2),
where µ = 1 and σ2 = 2; compute the sample mean. Repeat the above
simulation 500 times, plot the histogram of the 500 sample means
(does it mean that I can just use hist() method instead of plot()
method). Now repeat the 500 simulations for n = 1,000. Compare
these two sets of results with diﬀerent sample sizes, and discuss
it in the context...

Given a population with a mean of µ = 100 and a
variance σ2 = 12, assume the central limit
theorem applies when the sample size is n ≥ 25. A random
sample of size n = 52 is obtained. What is the probability
that 98.00 < x < 100.76?

Given a population with a mean of µ = 100 and a variance σ2 =
13, assume the central limit theorem applies when the sample size
is n ≥ 25. A random sample of size n = 28 is obtained. What is the
probability that 98.02 < x⎯⎯ < 99.08?

Suppose an x distribution has mean μ = 4. Consider two
corresponding x distributions, the first based on samples of size n
= 49 and the second based on samples of size n = 81.
(a) What is the value of the mean of each of the two x
distributions? For n = 49, μ x =
For n = 81, μ x =

Please answer with proper steps -
Suppose that a random sample of size n is drawn from a
population with mean µ = 220 and standard deviation σ = 20.
i. Determine the required sample size such that the standard
error of the sample mean is reduced to less than 3. [2 marks]
ii. Determine the required sample size if we want to be 90%
confident that the maximum error is 5.

Suppose an x distribution has mean μ = 2.
Consider two corresponding x distributions, the
first based on samples of size n = 49 and the second based
on samples of size n = 81.
(a) What is the value of the mean of each of the two x
distributions?
For n = 49, μx=
For n = 81, μx=
Suppose x has a distribution with μ = 54 and
σ = 5.
Find P(50 ≤ x ≤ 55). (Round your...

a. If ? ̅1 is the mean of a random sample of size n from a
normal population with mean ? and variance ?1 2 and ? ̅2 is the
mean of a random sample of size n from a normal population with
mean ? and variance ?2 2, and the two samples are independent, show
that ?? ̅1 + (1 − ?)? ̅2 where 0 ≤ ? ≤ 1 is an unbiased estimator
of ?.
b. Find the value...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 20 minutes ago

asked 30 minutes ago

asked 50 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago