1. What size sample will be needed to construct a 95% confidence interval on a ballot issue if the estimate must be 2% of the actual percent. This issue looks very close in the election.
2. A sample of 800 voters revealed that 52% of them would vote for a specific issue. Create and interpret a 95% confidence interval for the support of the issue. In the interpretation indicate what type of statement you can make about the issue passing. What is the error of the estimate for this problem? How could you decrease the size of the interval?
3. A student is trying to determine how much money a student in her
school spends when buying lunch in the cafeteria. She randomly selects 16 students who buy their lunch and records the amount that they spend. The following lists the results:
3.25 4.50 2.95 4.25 5.25 4.80 4.10 3.95
3.75 2.80 4.87 5.10 4.68 4.75 4.55 4.60
a. Construct a 95% confidence interval for the average amount spent on lunch.
b. What is the point estimate for the mean amount spent on lunch at this school?
c. What is the margin of error?
d. The school cafeteria claims that the average amount is $3.70. What comment can you make about this claim?
4. Bride's Magazine reported that the mean cost of a wedding is $19,000 with a standard deviation of $9400. If Bride's magazine wishes to construct a 95% interval estimate of the true mean cost, what is the recommended sample size if the margin of error is $1000?
5. The state department of agriculture is trying to determine the average corn yield for farmers in the state. They take a sample of 40 farmers and determine that the average yield was 151.2 bushels per acre. If the population standard deviation is 12.3 bushels per acre, create a 90% confidence interval for the mean yield in the state this season.
What is the margin of error? Create a 99% confidence interval for the mean yield per acre.