Verifying a Property of Variances

a. Find the variance for this population of x values: 5, 10, 15. (See Section 2-5 for the variance s2 of a population.)

b. Find the variance for this population of y values: 1, 2, 3.

c. List the population of all possible differences x 2 y, and find the variance of this population.

d. Use the results from parts (a), (b), and

(c) to verify that the variance of the differences between two independent random variables is the sum of their individual variances ( ). (This principle is used to derive the test statistic and confidence interval given in this section.)

e. How is the range of the differences x 2 y related to the range of the x values and the range of the y values?