Mean Absolute Deviation Use the same population of {2 min, 3 min, 8 min} from Exercise 45. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?

Solution 46BB

From the given information, the population of delay times consists of 2 minutes, 3 minutes, and 8 minutes.

The drawn samples of size 2 by with replacement from the given population of size 3 are with respective sample means 2, 2.5, 5, 2.5, 3, 5.5, 5, 5.5, and 8.

We know that, the sample absolute mean deviation found by

Therefore, the sample absolute mean deviation is 1.63 minutes.

We know that, the population absolute mean deviation found by

Therefore, the population absolute mean deviation is 2.443 minutes.