Deck 10: Sampling Distributions and Confidence Intervals for Proportio

Question 1

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

Answer 1

438

Question 2

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

Answer 2

0.1446 to 0.2954

Question 3

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

Answer 3

135

Question 4

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 5

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 6

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 7

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 13.4%.
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 8

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 9

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

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 11

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 12

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 13

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 14

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 15

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

Question 16

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 17

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.

Question 18

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