a. Test the following hypotheses with = .05 given that x = 405, s = 100,

a. Test the following hypotheses with α = .05 given that x̄ = 405, s = 100, and n = 1,000.

H0: µ = 400

H1: µ > 400

b. Repeat part (a) assuming that you know that the population standard deviation is σ = 100.

c. Explain why the conclusions produced in parts (a) and (b) are virtually identical.

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.