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

$n = 157 \\ \bar{X} = 146 \\ s = 27$

Assumption: population is not normal, σ² is unknown, α=0.01

$H_0 : μ=140 \\ H_1 : μ≠140$

Test Statistic:

$Z = \frac{\bar{X}-μ}{s/ \sqrt{n}} \\ Z = \frac{146-140}{27/ \sqrt{157}} \\ = \frac{6}{2.1548} \\ = 2.78$

Decision Rule:

we reject H₀ if Z>Z_1-α or Z<-Z_1-α

Z_0.99= 2.33 (from table)

2.78>2.33

Reject H₀

Hence, we can not conclude that the mean systolic blood pressure for a population of African-American is 140 mm Hg.