Question

When samples of the same size are taken from the same population, the following two properties apply:

- Sample proportions tend to be ______ .
- The mean of sample proportions is the same as the _____ .

Answer #1

Solution

Given that,

example

p = 0.5

1 - p = 0.5

n = 55

Sample proportions tend to be

- The mean of sample proportions is the same as the ____ p_ .

= p =0.5

note

= [p ( 1 - p ) / n] = [(0.) / ]

Suppose random samples of the same size are taken from two
different populations with the same mean but different standard
deviations. If you make two confidence intervals, one from each
sample, and these intervals have the same confidence level, how
will the confidence intervals differ? Explain.

Random samples of size n= 400 are taken from a
population with p= 0.15.
a.Calculate the centerline, the upper control
limit (UCL), and the lower control limit (LCL) for the p
chart.
b.Suppose six samples of size 400 produced the
following sample proportions: 0.06, 0.11, 0.09, 0.08, 0.14, and
0.16. Is the production process under control?

Using the following information:
For the first population: sample size of 30 taken from the
population, sample mean 1.32 , population variance 0.9734.
For the second population : sample size of 30 taken from the
population, sample mean 1.04,
population variance 0.7291.
Find a 90% confidence interval for the difference between the
two population means.

consider the following results frmo two independent random
samples taken from two populations. assume that the variances are
NOT equal.
Population 1
population 2
sample size
50
50
sample mean
35
30
sample variance
784
100
a) what is the "degrees of freedom" for these data?
b) what is the 95% confidence interval difference of the
population means?

Consider random samples of size 82 drawn from population
A with proportion 0.45 and random samples of size 64 drawn
from population B with proportion 0.11 .
(a) Find the standard error of the distribution of differences
in sample proportions, p^A-p^B.
Round your answer for the standard error to three decimal
places.
standard error = Enter your answer in accordance to the question
statement
(b) Are the sample sizes large enough for the Central Limit
Theorem to apply?...

Consider random samples of size 58 drawn from population
A with proportion 0.78 and random samples of size 76 drawn
from population B with proportion 0.68 .
(a) Find the standard error of the distribution of differences
in sample proportions, p^A-p^B.
Round your answer for the standard error to three decimal
places.
standard error = Enter your answer in accordance to the question
statement
(b) Are the sample sizes large enough for the Central Limit
Theorem to apply?
Yes
No

Consider the following results for independent samples taken
from two populations.
sample 1
sample 2
n1=500
n2=200
p1= 0.42
p2= 0.34
a. What is the point estimate of the difference between the two
population proportions (to 2 decimals)?
b. Develop a confidence interval for the difference between the
two population proportions (to 4 decimals). (______to _______)
c. Develop a confidence interval for the difference between the
two population proportions (to 4 decimals). (______to________)

The Central Limit Theorem says that when sample size n is taken
from any population with mean μ and standard deviation σ when n is
large, which of the following statements are true?
The distribution of the sample mean is approximately
Normal.
The standard deviation is equal to that of the population.
The distribution of the population is exactly Normal.
The distribution is biased.

Consider the following results for independent samples taken
from two populations.
Sample 1
Sample 2
n1 = 500
n2= 200
p1= 0.45
p2= 0.34
a. What is the point estimate of the difference
between the two population proportions (to 2 decimals)?
b. Develop a 90% confidence interval for the
difference between the two population proportions (to 4 decimals).
Use z-table.
to
c. Develop a 95% confidence interval for the
difference between the two population proportions (to 4 decimals).
Use z-table....

Consider the following results for independent samples taken
from two populations.
Sample 1
Sample 2
n1 = 500
n2= 300
p1= 0.43
p2= 0.36
a. What is the point estimate of the difference
between the two population proportions (to 2 decimals)?
b. Develop a 90% confidence interval for the
difference between the two population proportions (to 4 decimals).
Use z-table.
to
c. Develop a 95% confidence interval for the
difference between the two population proportions (to 4 decimals).
Use z-table....

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