Deck 11: Confidence Intervals for Proportions

Question 1

They actually select a random sample of 525 employment records, and find that 229 of
the people are females. Construct the 90% confidence interval.

Answer 1

4722)

Question 2

Find and interpret the margin of error.
Automobile mechanics conduct diagnostic tests on 150 new cars of particular make
And model to determine the extent to which they are affected by a recent recall due to
Faulty catalytic converters. They find that 42 of the new cars tested do have faulty
Catalytic converters. What is the margin of error for a 99% confidence interval based on
These sample results?

A) 0.0366
B) 0.0719
C) 0.0944
D) 0.1140
E) 0.2876

Answer 2

B

Question 3

Interpret the confidence interval in this context.

Answer 3

22% of the employment records from
the United States labor force are female.

Question 4

Find and interpret the margin of error.
EU (European Union) countries report that 46% of their labor force is female. The
United Nations wants to determine if the percentage of females in the U.S. labor force is
The same. Based on a sample of 500 employment records, representatives from the
United States Department of Labor find that the 95% confidence interval for the
Proportion of females in the U.S. labor force is .357 to .443. If the Department of Labor
Wishes to tighten its interval, they should

A) increase the confidence level.
B) decrease the sample size.
C) increase the sample size.
D) Both A and B
E) Both A and C

Question 5

Interpret the confidence interval in this context.

Question 6

Find and interpret the margin of error.
EU (European Union) countries report that 46% of their labor force is female. The
United Nations wants to determine if the percentage of females in the U.S. labor force is
The same. Based on a sample of 500 employment records, representatives from the
United States Department of Labor find that 240 are female. What is the margin of error
For the 95% confidence interval of the proportion of females in the U.S. labor force?

A) 0.022
B) 0.044
C) 0.036
D) 0.056
E) 0.089

Question 7

Should the Quality Control Department conclude that the percentage of rework for the
electrical components is lower than the rate of 12% for non-electrical components?
Explain.

Question 8

Find the sample size.
The U.S. Department of Labor wants to estimate the percentage of females in the labor
Force to within ±5% with 90% confidence. As a planning value they use 46%, the
Reported percentage of females in the labor force of EU (European Union) countries.
How many employment records should be sampled?

A) 121
B) 269
C) 451
D) 382
E) 1000

Question 9

Check assumptions / conditions for confidence intervals.
Which of the following is not an assumption and / or condition required for
Constructing a confidence interval for the proportion?

A) Randomization condition
B) Linearity condition
C) Success / Failure condition
D) 10% condition
E) None of the above

Question 10

Find and interpret the confidence interval.
EU (European Union) countries report that 46% of their labor force is female. The
United Nations wants to determine if the percentage of females in the U.S. labor force is
The same. Representatives from the United States Department of Labor select a random
Sample of 525 from over 10,000 employment records on file and find that 229 are female.
The 90% confidence interval for the proportion of females in the U.S. labor force is

A) 0.3998 to 0.4722
B) 0.2747 to 0.5973
C) 0.1776 to 0.6944
D) 0.4235 to 0.5679
E) 0.1243 to 0.7100

Question 11

Are the assumptions and conditions for constructing a confidence interval met?
Explain.

Question 12

Explain what 99% confidence means in this context.

Question 13

Find and interpret the confidence interval.
Automobile mechanics conduct diagnostic tests on 150 new cars of particular make
And model to determine the extent to which they are affected by a recent recall due to
Faulty catalytic converters. They find that 42 of the new cars tested do have faulty
Catalytic converters. The 99% confidence interval for the true proportion of new cars
With faulty catalytic converters is

A) 0.1856 to 0.3744
B) 0.2434 to 0.3166
C) 0.2081 to 0.3519
D) 0.1660 to 0.3940
E) 0.1243 to 0.4123

Question 14

Explain what 90% confidence means in this context.

Question 15

Find and interpret the confidence interval.
A recent poll of 120 adults who frequent the local farmer's market found that 54 have
Purchased reusable cloth bags for their groceries. The 95% confidence interval for the
Proportion of adults who have purchased reusable cloth bags is

A) 0.361 to 0.539
B) 0.4046 to 0.4954
C) 0.4383 to 0.4617
D) 0.205 to 0.525
E) 0.3856 to 0.4896

Question 16

Find and interpret the confidence interval.
EU (European Union) countries report that 46% of their labor force is female. The
United Nations wants to determine if the percentage of females in the U.S. labor force is
The same. Based on a sample of 500 employment records, representatives from the
United States Department of Labor find that the 95% confidence interval for the
Proportion of females in the U.S. labor force is .357 to .443. Which of the following is the
Correct interpretation?

A) The percentage of females in the U.S. labor force is between 35.7% and 44.3%.
B) We are 95% confident that between 35.7% and 44.3% of the persons in the U.S. labor force is female.
C) The margin of error for the true percentage of females in the U.S. labor force is between 35.7% and 44.3%.
D) All samples of size 500 will yield a percentage of females in the U.S. labor force that falls within 35.7% and 44.3%.
E) None of the above.

Question 17

They actually select a random sample of 450 electrical components and find that 46 of
those had to be reworked. Create the confidence interval.

Question 18

Find the sample size.
The U.S. Department of Labor wants to estimate the percentage of females in the
Labor force to within ±2% with 90% confidence. As a planning value they use 46%, the
Reported percentage of females in the labor force of EU (European Union) countries.
How many employment records should be sampled?

A) 121
B) 269
C) 451
D) 382
E) 1681

Question 19

Are the assumptions and conditions for constructing a confidence interval met?
Explain.

Question 20

Should representatives from the Department of Labor conclude that the percentage of
females in the U.S. labor force is lower than Europe's rate of 46%? Explain.

Question 21

Find the sample size.
The Quality Control Department wants to estimate the true percentage of rework for
Electrical components to within ±4%, with 99% confidence. Based on similar past
Studies, the percentage of rework was found to be 12%. How many components should
They sample?

A) 651
B) 1000
C) 344
D) 438
E) 579

Question 22

Find and interpret the confidence interval.
One division of a large defense contractor manufactures telecommunication
Equipment for the military. This division reports that 12% of non-electrical components
Are reworked. Management wants to determine if this percentage is the same as the
Percentage rework for the company's electrical components. Based on a random sample
Of 450 electrical components, they find that 46 had to be reworked. The 99% confidence
Interval is

A) 0.0652, 0.1388
B) 0.0432, 0.1608
C) 0.0763, 0.1277
D) 0.0541, 0.1499
E) None of the above.

Question 23

Find the sample size.
The unemployment rate of persons with a disability is typically higher than for those
With no disability. Recent statistics report that the national rate of unemployment among
This group is 14.5%. The local government of a small city wants to determine the rate in
Its region to within ±5%, with 90% confidence. How many individuals with disabilities
Should they sample?

A) 135
B) 191
C) 354
D) 678
E) 981

Question 24

Find the sample size.
The unemployment rate of persons with a disability is typically higher than for those
With no disability. Recent statistics report that the national rate of unemployment among
This group is 14.5%. The local government of a small city wants to determine the rate in
Its region to within ±5%, with 95% confidence. How many individuals with disabilities
Should they sample?

A) 135
B) 191
C) 354
D) 678
E) 981

Question 25

Find and interpret the margin of error.
A recent poll of 120 adults who frequent the local farmer's market found that 54 have
Purchased reusable cloth bags for their groceries. Based on these data, what is the margin
Of error for a 95% confidence interval of the proportion of adults who have purchased
Reusable cloth bags?

A) 0.0454
B) 0.0117
C) 0.089
D) 0.075
E) 0.0432

Question 26

Find and interpret the confidence interval.
One division of a large defense contractor manufactures telecommunication
Equipment for the military. This division reports that 12% of non-electrical components
Are reworked. Management wants to determine if this percentage is the same as the
Percentage rework for the company's electrical components. The Quality Control
Department plans to check a random sample of the over 10,000 electrical components
Manufactured across all divisions. The resulting 95% confidence interval based on these
Data is .0758 to .1339. Which of the following is the correct interpretation?

A) The percentage of electronic components that are reworked is between 7.6% and
B) We are 95% confident that between 7.6% and 13.4% of electrical components are reworked.
C) The margin of error for the true percentage of electrical components that are reworked is between 7.6% and 13.4%.
D) All samples of size 450 will yield a percentage of reworked electrical components that falls within 7.6% and 13.4%.
E) None of the above.

Question 27

Find and interpret the confidence interval.
Recent statistics report that the national rate of unemployment among persons with
Disabilities is 14.5%. The local government of a small city samples 200 individuals with
Disabilities and finds that 44 are unemployed. The 99% confidence interval for the
Unemployment rate among persons with disabilities in their city is

A) 0.1646 to 0.2754
B) 0.1735 to 0.2665
C) 0.1446 to 0.2954
D) 0.1332 to 0.3298
E) 0.1145 to 0.4374

Question 28

Find and interpret the confidence interval.
One division of a large defense contractor manufactures telecommunication
Equipment for the military. This division reports that 12% of non-electrical components
Are reworked. Management wants to determine if this percentage is the same as the
Percentage rework for the company's electrical components. The Quality Control
Department plans to check a random sample of the over 10,000 electrical components
Manufactured across all divisions. The 95% confidence interval based on this data is
)0758 to .1339. Should management conclude that the percentage of rework for
Electrical components is lower than the rate of 12% for non-electrical components?

A) Yes, because the lower limit of the confidence interval is 7.6%.
B) Yes, because 12% is contained with the 95% confidence interval.
C) No, because 12% is contained with the 95% confidence interval.
D) No, because the upper limit of the confidence interval is 13.4%.
E) None of the above.