Let’s Summarize

• A confidence interval is formed by taking a single value (point estimate) and adding and subtracting an error bound (margin of error).
• The formula for creating a confidence interval for a mean is based on a normal distribution if the population standard deviation is known. If the population standard deviation is not known, then a t-distribution is used with degrees of freedom (df) equal to the sample size minus 1.
• The formula for creating a confidence interval for a proportion is based on a normal distribution.
• The size of the error bound is based on the confidence level, standard deviation (or standard error) and the sample size.
• The confidence level refers to the long-run success rate of all possible confidence intervals from all possible random samples of a given sample size.
• For a given confidence level, intervals are narrower for larger sample sizes.
• For a given sample size, intervals are wider for larger confidence levels.
• When constructing a confidence interval for a proportion, the “plus-four” method of adding two additional successes and two additional failures can be used to produce more accurate confidence intervals.