a. Test the following hypotheses with   .05 given that , s  100, and n  1,000.

b. Repeat part

(a) assuming that you know that the population standard deviation is   100.

c. Explain why the conclusions produced in parts

(a) and

(b) are virtually identical.

Applications The following exercises may be answered manually or with the assistance of a computer. The data are stored in files. Assume that the random variable is normally distributed.