Plotting the Means of Samples

Suppose you plot the mean of each of your height samples on a graph, and drawing a line each way of the mean of each sample to represent 2 standard deviations. If you were to do this for 50 of the samples, you might end up with an image like the one below.

The image is a screen capture from the interactive applet at Bedford, Freeman, and Worth Publishing Group's website

At the top of the image is a normal curve. Each of the lines below the curve has a length that represents a 95% confidence interval, centered on the mean (in red) of the sample.

a. What is indicated by the lines that are all red in color?

The lines that are colored entirely red have a mean that is greater than 2 standard deviations away from the population mean. In other words, the mean of those two samples was not within the stated confidence interval (95%).

b. What value is indicated by the vertical red center line on each interval?

The vertical red center line represents the mean of each sample.

c. What does the "percent hit" number mean? How would it change if you were to continue taking more and more samples of 60 each?

The “percent hit” number indicates the percentage of times that the population mean was included in the confidence interval of sample means. If you were to continue plotting sample means and confidence intervals, the percent hit would approach 95%. In fact, here is the same graph after 1000 sample runs: