Question

Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of African-American is 140.

Answer 1

n=157 , sample mean=146, s=27, α=0.01

$Z = \dfrac{{\overline{X}-\mu_0}}{\frac{s}{\sqrt{n}}}=\dfrac{146-140}{\frac{27}{\sqrt{157}}} = 2.78$

We reject H₀ if Z>Z_1-α = Z_0.99= 2.33

Hence, we can conclude that the mean systolic blood pressure for a population of African-American is greater than 140 mm Hg.