The applet below illustrates the concept of constructing confidence intervals for proportions (a 1-proportion z-interval). Set the population proportion, sample size, and confidence level using the sliders. There are 100 confidence intervals at your chosen confidence level, based on 100 random samples of your chosen sample size, from a population with your chosen proportion. On average, the percentage of confidence intervals that contain the population proportion will be equal to the chosen confidence level. The following applet is for you to play and explore. Once you have experimented with different proportions, sample sizes, and confidence levels, proceed to the questions below.

To interpret a confidence level of 0.95 we could say the following: If we were to select many random samples from a population and construct a 95% confidence interval using each sample, about 95% of the intervals would capture the true population proportion.

A confidence interval consists of two parts. A point estimate is at the center of our interval and is a statistic that provides an estimate of a population parameter. The margin of error is the distance from the point estimate to the edge of our confidence interval. Thus, the difference between the point estimate and the true parameter value will be less than the margin of error in C% of all samples, where C is the confidence level.