Question

Describe the distribution of sample means (i.e., shape, measure of
central tendency, and variability) for samples of size n = 49
selected from a population with mean µ = 14 and standard deviation
σ = 7. Be specific and calculate as necessary.

Answer #1

Let X be the random variable.

The sample size is

As per the central limit theorem, when the sample size is large (i.e. greater than 30), the distribution of the sample means is approximately normal with mean, and variance, .

The aim is to find the sampling distribution for the random variable .

As per the given information, and the description above, follows the normal distribution with parameters:

Random samples of size n were selected from a
normal population with the means and variances
given here.
n = 25, μ = 12, σ2 = 9
Describe the shape of the sampling distribution of the sample
mean.
a. The distribution is normal
b. The distribution is skewed left
c. The distribution is bimodal
d. The distribution is uniform
e. The distribution is skewed right
Find the mean and the standard error of the sampling
distribution of the sample mean....

Suppose
Jack
and
Diane
are each attempting to use a simulation to describe the sampling
distribution from a population that is skewed
right
with mean
50
and standard deviation
15.
JackJack
obtains 1000 random samples of size
n=55
from the population, finds the mean of the means, and
determines the standard deviation of the means.
Diane
does the same simulation, but obtains 1000 random samples of
size
n=40
from the population. Complete parts (a) through (c) below.
a) Describe the...

Apply the Central Limit Theorem for Sample Means A population of
values has a normal distribution with μ = 220 and σ = 33.8. You
intend to draw a random sample of size n = 35.
Find the probability that a single randomly selected value from
the population is less than 224.

1.What is the best way to describe the expected value of M?
a.The sample standard deviation
b.The standard deviation for the distribution of sample
means
c.A sample mean
d.The mean of the distribution of sample means
2.Which combination of factors is more likely to produce small
standard error?
a.σ = 5; n = 25
b.σ = 5; n = 100
c.σ = 10; n = 25
d.σ = 10; n = 100
3.The standard error is written out with which...

The Central Limit Theorem allows us to make predictions about
where a sample mean will fall in a distribution of sample means.
One way it does this is by explaining (using a formula) how the
shape of the distribution will change depending on the sample size.
What part of the Central Limit Theorem tells us about the shape of
the distribution?
The part that explains that there is no standardized table you
can use to find probabilities once you use...

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?

Use the formula to find the standard error of the distribution
of differences in sample means, .
Samples of size 120 from Population 1 with
mean 87 and standard deviation 14 and samples
of size 85 from Population 2 with mean 71 and
standard deviation 17
Round your answer for the standard error to two decimal
places.
standard error
=

Apply the Central Limit Theorem for Sample
Means
A population of values has a normal distribution with μ=77 and
σ=9.2. You intend to draw a random sample of size n=30.
Find the probability that a sample of size n=30n=30 is randomly
selected with a mean less than 76.8.
P(M < 76.8) =
Enter your answers as numbers accurate to 4 decimal places.
Answers obtained using exact z-scores or
z-scores rounded to 3 decimal places are accepted.

Samples of n = 25 scores are selected from a population. If the
distribution of sample means has an expected value of 50 and a
standard error of 2, what are the mean and the standard deviation
for the population?

Samples of n = 16 scores are selected from a population. If the
distribution of sample means has an expected value of 40 and a
standard error of 2, what is the mean and the standard deviation
for the population?
***please provide step by step details

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