Exam 16: Confidence Intervals for Proportions

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

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.

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.

An advertising firm wants to confirm estimates that 18% of households will buy something on the internet next year.What sample size will produce a margin of error of 7% with 90% confidence level?

A company has surveyed a sample of its employees to find out how many might take advantage of a weight loss program.The table below shows the results.For which of the groups could we use our methods of inference to determine a 95% confidence interval for the proportion of employees who would be willing to participate in the program? Group Number of Employees Number Surveyed Percent to Participate Building C 5200 250 8\% Building B 1190 150 6\% Building A 248 20 9\%

The management of a water park has concerns about the chlorine level of 0.4% mg/mL increasing to an unsafe level.The management tests the hypothesis that the park's chlorine proportions have remained the same.An independent agency ran a test on a random sample size of $10000$ and found the chlorine level at 0.5% mg/mL.Create a 95% confidence interval for the proportion of chlorine in the water.

In a poll of 553 voters in a certain city,64% said that they supported the NDP in an upcoming election.The margin of error in the poll was reported as 4 percentage points (with a 95% degree of confidence).Make a statement about the adequacy of the sample size for the given margin of error.

A survey of shoppers is planned to see what percentage use credit cards.Prior surveys suggest 56% of shoppers use credit cards.How many randomly selected shoppers must we survey in order to estimate the proportion of shoppers who use credit cards to within 1% with 95% confidence?

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 random sample of 64 statistics students at a small college were given a surprise quiz out of 40 marks.The average score was 27 with a standard deviation of 5.Find a 95% confidence interval for the mean quiz score for all statistics students at this college.

How tall is the average student on your campus? To determine this,you measure the height of a random sample of 200 students,finding a mean height of 166.60 cm and a standard deviation of 5.64 cm.Construct a 90% confidence interval for the mean height of your fellow students.

In a survey of 1,000 television viewers,40% said they watch network news programs.For a 99% confidence level,the margin of error for this estimate is 3.99%.If we only want to be 90% confident,how will the margin of error change?

A local bank needs information concerning the checking account balances of its local customers.A random sample of 144 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29.Find a 98% confidence interval for the true mean checking account balance for local customers.

A poll of 2841 registered voters in a certain town indicated that 70% would vote for the Liberal Party of Canada.The margin of error for this poll was 2%.

A researcher wants to estimate the mean cholesterol level of people in his city.A random sample of 221 people yields an average cholesterol level of 219,with a margin of error of ±12.Assume the researcher used a confidence level of 90%.

Of 88 adults selected randomly from one town,60 have health insurance.Construct a 90% confidence interval for the percentage of all adults in the town who have health insurance.

In a survey of 1,000 television viewers,40% said they watch network news programs.For a 90% confidence level,the margin of error for this estimate is 2.5%.If we want to be 99% confident,how will the margin of error change?

How many unpopped kernels are left when you pop a bag of microwave popcorn? Quality control personnel at Yummy Popcorn take a random sample of 80 bags of popcorn.They pop each bag in a microwave and then count the number of unpopped kernels.The following interval is produced: t-interval for μ : with 99% Confidence, 11 < μ(unpopped)< 25

A credit union took a random sample of 400 accounts and obtained the following 90% confidence interval for the mean checking account balance at the institution: $2185 < μ(balance)< $3846.

According to the 2004 Canadian Community Health Survey,23.1% of Canadians aged 18 or older were considered obese; that is,they had a body mass index (BMI)of 30 or higher.Suppose a current survey in 2014 of 1000 random Canadians found that 245 were obese.Create a 95% confidence interval for the proportion of Canadians that are currently obese.