Exam 11: Confidence Intervals for Proportions

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. -The Quality Control Department wants to estimate the true percentage of rework for electrical components to within 4%, with 99% confidence. How many components should they sample?

A human resources manager wishes to estimate the proportion of employees in her large company who have supplemental health insurance. What sample size should she select if she wants 95% confidence and a margin of error of 0.01?

A study was recently conducted at a major university to estimate the difference in the proportion of business school and non-business school graduates who go on to a higher degree program within five years of graduation A random sample of 400 business school graduates showed that 75 had gone to graduate school, while in a random sample of 500 non-business graduates, 137 had done so. The standard error for the difference in the proportions of the two groups is

City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. They take a sample of 400 visitors and find that 100 are on a second visit. The 95% confidence interval is

Consider the following to answer the question(s) below: EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same. Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force. -Explain what 90% confidence means in this context.

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

City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. From previous experience they believe the proportion is not larger than 20 percent. They want to estimate the proportion to within 0.04 percentage points with 95 % confidence. The sample size they should use is

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. 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 0.0742 to 0.1302. Which of the following is the correct interpretation?

Consider the following to answer the question(s) below: EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same. Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force. -Should representatives from Statistics Canada conclude that the percentage of females in the Canadian labour force is lower than European rate of 46%? Explain.

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. -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.

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. -Are the assumptions and conditions for constructing a confidence interval met? Explain.

A sample of 250 people resulted in a confidence interval estimate of between 0.14 and 0.20 for the proportion of people who believe that tax increase proposed by the federal government is justified. Based on this information, what was the confidence level used in this estimation?

Consider the following to answer the question(s) below: EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same. Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force. -If Statistics Canada wishes to tighten its interval, they should

Consider the following to answer the question(s) below: EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same. Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force. -They actually select a random sample of 525 employment records, and find that 229 of the people are females. The 90% confidence interval is

City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. Suppose they find they need a sample size of 15,000 people to achieve a margin of error of 0.01 percentage points with 99 % confidence. This sample is too large to be practical. How can they reduce the sample size?

City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. They take a sample of 400 visitors and find that 100 are on a second visit. The 99% confidence interval is 0.1942 to 0.3058. The correct interpretation of the interval is

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. -They actually select a random sample of 450 electrical components and find that 46 of those had to be reworked. Create the 99% confidence interval.

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. -Explain what 99% confidence means in this context.

Which of the following is not an assumption / condition required for constructing a confidence interval for the proportion?

Consider the following to answer the question(s) below: 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 electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions. -Interpret the confidence interval in this context.