Refer to the Why Divide by n - 1 applet. The first applet on the page randomly selects sample of n = 3 from a population in which the standard deviation is σ = 29.2.

a. A sample consisting of n = 3 observations will appear. Use your calculator to verify the values of the standard deviation when dividing by n - 1 and n as shown in the applet.

b. Calculate the average of the two standard deviations (dividing by n - 1) from parts a and b. Repeat the process for the two standard deviations (dividing by n). Compare your results to those shown in red on the applet.

c. You can look at how the two estimators in part a behave “in the long run” by clicking or a number of times, until the average of all the standard deviations begins to stabilize. Which of the two methods gives a standard deviation closer to σ = 29.2?

d. In the long run, how far off is the standard deviation when dividing by n?