Are older men shorter than younger men?

According to the National Health Statistics Reports, the mean height for U.S. men is 69.4 inches. In a sample of 300 men between the ages of 60 and 69, the mean height was x̄ = 69.0 inches. Public health officials want to determine whether the mean height μ for older men is less than the mean height of all adult men.

a. State the appropriate null and alternate hypotheses.

b. Assume the population standard deviation to be

σ = 2.84 inches. Compute the value of the test statistic.

c. State a conclusion. Use the α = 0.01 level of significance.