Download Online 11 - Sections 8.1 and 8.2

Online 11 - Sections 8.1 and 8.2-Doug Ensley
Student: _____________________
Date: _____________________
Instructor: Doug Ensley
Course: MAT117 01 Applied Statistics Ensley
Assignment: Online 11 - Sections 8.1
and 8.2
1. One question on a survey asked, "Do you think that it should be government's responsibility to reduce income differences
between the rich and the poor?" Of the possible responses, 605 picked "definitely or probably should be," and 633 picked
"probably or definitely should not be." a) Find the point estimate of the population proportion who would answer "definitely
or probably should be." The margin of error of this estimate is 0.03. b) Explain what this represents.
a) What is the point estimate of the population proportion who would answer "definitely or probably should be?"
(Round to three decimal places as needed.)
b) Explain what the margin of error represents.
A. The margin of error of 0.03 is a prediction that the sample point falls within 0.03 of the population
proportion.
B. The margin of error of 0.03 is a prediction that the sample point falls outside 0.03 of the
population proportion.
C. The margin of error of 0.03 is a prediction that the sample point falls within 0.95 of the population
proportion.
2. When 508 subjects were asked, "Do you believe in heaven?" the proportion who answered yes was 0.77. The standard
deviation of this point estimate is 0.02.
a. Find and interpret the margin of error for a 95% confidence interval for the population proportion of people who believe in
heaven.
b. Construct the 95% confidence interval. Interpret it in context.
a. Find the margin of error for a 95% confidence interval for the population proportion of people who believe in heaven.
(Round to two decimal places as needed.)
Interpret the margin of error.
A. With 95% confidence, it can be stated that the population proportion is more than half a margin
of error lower or half a margin of error higher than the reported sample proportion.
B. With 95% confidence, it can be stated that the population proportion is more than one margin of
error lower or one margin of error higher than the reported sample proportion.
C. With 95% confidence, it can be stated that the population proportion is no more than half a
margin of error lower or half a margin of error higher than the reported sample proportion.
D. With 95% confidence, it can be stated that the population proportion is no more than one margin
of error lower or one margin of error higher than the reported sample proportion.
b. The confidence interval goes from
to
.
(Round to two decimal places as needed.)
Interpret the confidence interval in context.
A. This interval contains the value for the proportion of people who believe in heaven 95% of the
time.
B. This is the interval containing the most believable values for the proportion of people who believe
in heaven.
C. This is the interval containing the sample median of people who believe in heaven..
D. This is the interval containing all the values for the proportion of people who believe in heaven.
1 of 5
Online 11 - Sections 8.1 and 8.2-Doug Ensley
3. A survey asked, "During the last year, did anyone take something from you by using force − such as a stickup, mugging, or
threat?" Of 963 subjects, 15 answered yes and 948 answered no.
a. Find the point estimate of the proportion of the population who were victims.
b. Find the standard error of this estimate.
c. Find the margin of error for a 95% confidence interval.
d. Construct the 95% confidence interval for the population proportion. Can you conclude that fewer than 10% of all adults
were victims?
a. Find the point estimate of the proportion of the population who were victims.
p=
(Round to five decimal places as needed.)
b. Find the standard error of this estimate.
se =
(Round to five decimal places as needed.)
c. Find the margin of error for a 95% confidence interval.
(Round to five decimal places as needed.)
d. Construct the 95% confidence interval for the population proportion.
(
,
) (Round to five decimal places as needed.)
Can you conclude that fewer than 10% of all adults were victims?
A. No, more than 10% of all adults were victims.
B. Yes, fewer than 10% of all adults were victims.
C. No conclusion can be drawn by using the 95% confidence interval.
2 of 5
Online 11 - Sections 8.1 and 8.2-Doug Ensley
4. When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the
environment, 337 of 1130 subjects said yes.
a. Find the point estimate of the proportion of the population who would answer yes.
b. Find the margin of error for a 95% confidence interval. c. Construct the 95% confidence interval for the population
proportion. What do the numbers in this interval represent? d. State and check the assumptions needed for the interval in
(c) to be valid.
a. Find the point estimate of the proportion of the population who would answer yes.
p=
(Round to five decimal places as needed.)
b. Find the margin of error for a 95% confidence interval.
(Round to five decimal places as needed.)
c. Construct the 95% confidence interval for the population proportion.
(
,
) (Round to five decimal places as needed.)
What do the numbers in this interval represent?
A. The numbers represent the most believable values for the population proportion.
B. The probability a surveyed individual would answer no falls in the confidence interval.
C. The probability a surveyed individual would answer yes falls in the confidence interval.
d. State and check the assumptions needed for the interval in (c) to be valid.
A. There are at least 30 observations.
B. The data must be obtained randomly and the number of observations must be greater than 30.
C. The data must be obtained randomly, and the expected numbers of successes and failures must
both be at least 15.
D. The data must be obtained randomly.
E. There are at least 15 successes and 15 failures expected.
3 of 5
Online 11 - Sections 8.1 and 8.2-Doug Ensley
5. A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all
right for the wife to refuse to have children?" Of 734 subjects, 567 said yes.
a. Find a 99% confidence interval for the population proportion who would say yes.
(
,
) (Round to four decimal places as needed.)
Can you conclude that the population proportion exceeds 75%? Why?
A. Yes, we can conclude that the population proportion exceeds 75%, because 75% is above the
lowest believable value of the confidence interval.
B. No, we cannot conclude that the population proportion exceeds 75% because 75% is above the
lowest believable value of the confidence interval.
C. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the
lowest believable value of the confidence interval.
D. No, we cannot conclude that the population proportion exceeds 75% because 75% is below the
lowest believable value of the confidence interval.
b. Without doing any calculations, explain whether the interval in (a) would be wider or narrower than a 95% confidence
interval for the population proportion who would say yes.
The 99% confidence interval would be narrower than a 95% confidence interval.
The 99% confidence interval would be wider than a 95% confidence interval.
4 of 5
Online 11 - Sections 8.1 and 8.2-Doug Ensley
1.
0.489
A. The margin of error of 0.03 is a prediction that the sample point falls within 0.03 of the population proportion.
2.
0.04
D.
With 95% confidence, it can be stated that the population proportion is no more than one margin of error lower or one margin
of error higher than the reported sample proportion.
0.73
0.81
B. This is the interval containing the most believable values for the proportion of people who believe in heaven.
3.
0.01558
0.00399
0.00782
0.00776
0.0234
B. Yes, fewer than 10% of all adults were victims.
4.
0.29823
0.02667
0.27156
0.3249
A. The numbers represent the most believable values for the population proportion.
C.
The data must be obtained randomly, and the expected numbers of successes and failures must both be at least 15.
5.
0.7326
0.8124
B.
No, we cannot conclude that the population proportion exceeds 75% because 75% is above the lowest believable value of the
confidence interval.
The 99% confidence interval would be wider than a 95% confidence interval.
5 of 5