Exam 16: Confidence Intervals for Proportions

You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.From your sample of 15 gas stations,you calculate a 95% confidence interval of ($1.34,$1.40)

A political party is interested in finding out what kind of popular support they might expect on an environmental initiative.Similar issues have gotten 87% support.The committee will set up a polling program to assure 95% confidence that the margin of error is less than 9%.What sample size will suffice?

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.

A newspaper reports that 58% of farmers are planning to plant genetically modified crops this year.The article adds that the poll is based on a random sample of 798 farmers and has a margin of error of 4.5%.

A survey of 300 students at York University revealed that 112 favour an NDP candidate for M.P.Construct a 98% confidence interval for the percentage of all York University students who favour an NDP candidate.

A pollster wishes to estimate the true proportion of voters in Ottawa,Ontario,who support the Conservative party.How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to within 4%?

A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Create a 95% confidence interval for the proportion of participant weight loss.

Of 125 adults selected randomly from one town,28 of them smoke.Construct a 99% confidence interval for the percentage of all adults in the town who smoke.

Of 314 randomly selected medical students,25 said that they planned to work in a rural community.Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community.

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 Statistics instructor wishes to estimate the proportion of first year statistics students that are over 30 years old.In his current class of 32,there are 2 students over 30 years old.Find a "Plus Four" 95% confidence interval for the true proportion.

When 278 college students are randomly selected and surveyed,it is found that 110 own a car.Construct a 99% confidence interval for the percentage of all college students who own a car.

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.

In April of 2011,the unemployment rate in Canada was reported to be 7.6%.Suppose that Statistics Canada claims that the current unemployment rate is lower than that of April 2011.Suppose a test was conducted on current unemployment and a random sample size of 1000 and found unemployment at 3.8%.Create a 95% confidence interval for the proportion of unemployment.

A survey found that 79% of a random sample of 1024 Canadian adults approved of cloning endangered animals.Find the margin of error for this survey if we want 90% confidence in our estimate of the percent of Canadian adults who approve of cloning endangered animals.

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%.

In a poll of 2778 voters in a certain city,77% said that they supported the Conservative Party of Canada.The margin of error in the poll was reported as 6 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 company hopes to improve its engines,setting a goal of no more than 3% of customers using their warranty on defective engine parts.A random survey of 1200 customers found only 20 with complaints.Create a 95% confidence interval for the true level of warranty users among all customers.

What is the difference between the standard deviation and the standard error in the sampling distribution of a sample proportion?

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.