This problem is meant to illustrate, in yet another way, the concept of "degrees of freedom". We used this concept when calculating the sample standard deviation, and we will see it again during the semester, so it is important to have a good understanding of it.

x1 = 1.709

x2 = 1.3

a. Calculate the sample mean of the numbers in your sample (x1 and x2).

b. Calculate the sample variance of the numbers in your sample.

c. Calculate the sample variance in a different way: use in the denominator the sample size, in this case n = 2, as opposed to the correct number of degrees of freedom, n 1 = 1.

d. Calculate the sample variance in a different way: instead of the sample mean x , use the known population mean = 0. Use n 1 = 1 as the number of degrees of freedom.

e. Calculate the sample variance in yet another way: still use = 0 instead of x , but this time use n = 2 as the number of degrees of freedom.