A confidence interval is used when estimating sample data from population data.

Given: A box contains a large number of red and blue marbles, but the proportions are unknown. 100 marbles are drawn at random, and 40 turn out to be red. The SE% turns out to be 5%. True or False: The percentage of red marbles in the box can be estimated as 40%; the SE% is 5%.

Given: A box contains a large number of red and blue marbles, but the proportions are unknown. 100 marbles are drawn at random, and 40 turn out to be red. The SE% turns out to be 5%. True or False: The 95% confidence interval for the percentage of red marbles in the sample is 30% to 50%.

Given: A box contains a large number of red and blue marbles, but the proportions are unknown. 100 marbles are drawn at random, and 40 turn out to be red. The SE% turns out to be 5%. True or False: The 5% measures the likely size of the chance error in the 40%.

For cluster samples, in order to find the standard error, we use the Half-Sample method.