Confidence Intervals

Below, you see a normal-shaped distribution in blue, which represents a population with mean and a fixed standard deviation . The orange normal-shaped distribution represents the sampling distribution of the mean for random samples of a particular fixed sample size. Note: Remember that if the sample size is large enough, the Central Limit Theorem tells us that the sampling distribution will be approximately normal no matter the population's shape. The green line marks the value of the population mean, . Below the distributions, a visual representation of 50 SRSs and their corresponding confidence intervals can be seen. The red dot marks the sample mean, which is the center of the interval. The lines on each side of the dot show the span of the confidence interval. Intervals shown in red do not include the population mean (). Set the desired confidence level by dragging the slider. Click on the refresh button in the upper right corner to recalculate 50 new SRSs.