The James family has five children: Jocelyn (age 8), Alyse (age 8), Michael (age 14), Erica (age 16), and Sarah (age 18).

1. Complete the table by listing the 10 possible samples of size n = 2 from this population and calculate the sample mean age for each sample. The first column is completed for you.

Sample

n = 2

J, A

8

1. Create a sampling distribution of the sample mean age of samples of size 2.

1. What is the mean of the sampling distribution of the sample mean? What is the mean of the population?

1. Is the sample mean an unbiased estimator of the population mean? Justify your answer.

1. Suppose we had taken samples of size 3 instead of size 2. Would the variability of the sampling distribution of the sample mean be larger, smaller, or about the same? Justify your answer.