Exam 16: Confidence Intervals for Proportions

Data in 1980 showed that about 42% of one country's population had never smoked cigarettes.In 2004,a national health survey in this country interviewed a random sample of 3000 adults and found that 51% had never been smokers.Create a 95% confidence interval for the proportion in 2004 of this country's adults who had never been smokers.

How much fat do reduced fat cookies typically have? You take a random sample of 120 reduced-fat cookies and test them in a lab,finding a mean fat content of 4.2 grams.You calculate a 95% confidence interval and find that the margin of error is ±0.8 grams.

Five years ago,a company found that 8% of its employees commuted to work by car.A test for the current proportion of commuting employees was done on a random sample of 1000 employees,and found car commuting to be 12%.Create a 95% confidence interval for the proportion of employee commute by car.

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.Give the 95% confidence interval for the group(s)for which we could use our methods of inference for the proportion of employees who would be willing to participate in the program. Group Number of Employees Number Surveyed Percent to Participate Building A 5200 250 8\% Building B 1190 150 6\% Building C 248 20 9\%

A random sample of clients at a weight loss centre were given a dietary supplement to see if it would promote weight loss.The centre reported that the 100 clients lost an average of 47 pounds,and that a 95% confidence interval for the mean weight loss this supplement produced has a margin of error of ±9 pounds.

After conducting a survey,a researcher wishes to cut the standard error (and thus the margin of error)to $\frac { 1 } { 3 }$ of its original value.How will the necessary sample size change?

A recent poll of 500 residents in a large town found that only 36% were in favor of a proposed referendum to build a new high school.Find the margin of error for this poll if we want 90% confidence in our estimate of the percent of residents in favor of this proposed referendum.

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%.

How much fat do reduced fat cookies typically have? You take a random sample of 120 reduced-fat cookies and test them in a lab,finding a mean fat content of 3.2 grams and a standard deviation of 1.9 grams of fat.Create a 99% confidence interval for the mean grams of fat.

A laboratory tested 60 chicken eggs and found that the mean amount of cholesterol was 241 milligrams with s = 14.7 milligrams.Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

A study involves 673 randomly selected deaths,with 34 of them caused by accidents.Construct a 98% confidence interval for the percentage of all deaths that are caused by accidents.