Exam 11: Confidence Intervals for Proportions

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. -Statistics Canada wants to estimate the percentage of females in the Canadian labour force to within ±5% with 90% confidence. How many employment records should be sampled?

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 the federal government's proposed tax increase is justified. Based on this information, what was the confidence level used in this estimation?

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.

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?

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.

A financial analyst is interested in estimating the proportion of publicly traded companies on the Toronto Stock Exchange that have cash balances of more than 10 percent of the total assets of the company. A random sample of 100 companies shows that 13 had cash balances of more than 10 percent of assets. The 90 percent confidence interval estimate 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 percent confidence. This sample is too large to be practical. How can they reduce the sample size?

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?

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.

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.

The produce manager for a local Sobey's store is interested in estimating the percentage of apples that arrive on a shipment with bruises. A random sample of 150 apples showed 14 with bruises. Based on this information, what is the margin of error for a 95 percent confidence interval estimate?

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. -Statistics Canada wants to estimate the percentage of females in the Canadian labour force to within ±5%, with 90% confidence. How many employment records should be sampled?

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 percent confidence. The sample size they should use is

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 programme 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 95% confidence interval 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

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

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 Europe's rate of 46%? Explain.

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. -Suppose that Statistics Canada wants to be 90% confident of estimating the percentage of females in the labour force to within ±2% of the true percentage. To do this they would have to

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.