Exam 18: Confidence Intervals for Proportions

The real estate industry claims that it is the best and most effective system to market residential real estate.A survey of randomly selected home sellers in Ontario found that a 99% confidence interval for the proportion of homes that are sold by a real estate agent is 66% to 76%.Interpret the interval in this context.

A mayoral election race is tightly contested.In a random sample of 1,900 likely voters,1,007 said that they were planning to vote for the current mayor.Based on this sample,would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.

How tall is the average student on your campus? To determine this,you measure the height,in centimetres,of a random sample of 200 students and calculate the following confidence interval with 95% confidence: 155.72 < μ(height)< 181.20

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 210 people yields a mean cholesterol level of 224 and a standard deviation of 18.Construct a 95% confidence interval for the mean cholesterol level.

Among a sample of 100 students selected at random from one college,the mean number of siblings is 1.4 with a standard deviation of 1.3.Find a 95% confidence interval for the mean number of siblings for all students at this college.

Eighty randomly selected students took the calculus final.If the sample mean was 76 and the standard deviation was 8.1,construct a 99% confidence interval for the mean score of all students.

A mayoral election race is tightly contested.In a random sample of 1,100 likely voters,572 said that they were planning to vote for the current mayor.Based on this sample,would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.

A newspaper reports that the Prime Minister's approval rating stands at 60%.The article adds that the poll is based on a random sample of 1,040 adults and has a margin of error of 2.5%.

Of 346 items tested,12 are found to be defective.Construct a 98% confidence interval for the percentage of all such items that are defective.

A survey of 865 people in one city reveals that 408 have visited a Tim Hortons location in the past week.Construct a 95% confidence interval for the percentage of all people in this city who have visited a Tim Hortons location in the last week.

A newspaper reports that 62% of city residents have visited one of the city parks in the last year.The article adds that the poll is based on a random sample of 996 residents and has a margin of error of 2.5%.

A university's administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation.In previous years,the percentage averaged 13%.He wants the margin of error to be within 4% at a 99% confidence level.What sample size will suffice? Use 2.575 as the critical value for a 99% confidence interval.

Of 130 randomly selected adults,32 were found to have high blood pressure.Construct a 95% confidence interval for the percentage of all adults who have high blood pressure.

The real estate industry claims that it is the best and most effective system to market residential real estate.A survey of randomly selected home sellers in Ontario found that a 99% confidence interval for the proportion of homes that are sold by a real estate agent is 70% to 80%.Explain what "99% confidence" means in this context.

A poll of 565 home sellers found that 25.1% were trying to sell their home without a real estate agent.The margin of error for this poll was 3%.

After conducting a survey,a researcher wishes to cut the standard error (and thus the margin of error)to Of its original value.How will the necessary sample size change?

Of 290 employees selected randomly from one company,12.41% of them commute by carpooling.Construct a 90% confidence interval for the percentage of all employees of the company who carpool.

The real estate industry claims that it is the best and most effective system to market residential real estate.A survey of randomly selected home sellers in Ontario found that a 90% confidence interval for the proportion of homes that are sold by a real estate agent is 75% ± 6%.Explain why each of these conclusions is not correct. a)Between 69% and 81% of all homes in Ontario are sold by a real estate agent. b)90% of all random samples of home sellers in Ontario will show that 75% of homes are sold by a real estate agent. c)90% of all random samples of home sellers in Ontario will show that 69% to 81% of homes are sold by a real estate agent. d)We are 90% sure that between 69% and 81% of homes in this sample were sold by a real estate agent.

In a survey of 280 adults over 50,80% said they were taking vitamin supplements.Find the margin of error for this survey if we want a 99% confidence in our estimate of the percent of adults over 50 who take vitamin supplements.

A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective.How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 1.4%?