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 greater than 140. Use α=0.01.

Answer 1

Null hypothesis H₀: μ <= 140

Alternative hypotheses H₁: μ > 140

Critical value at 0.01 significance level with 156 d.f. is 2.35.

$t = \frac{146 – 140}{\frac{27}{\sqrt{157}}} = 2.78$

Since test statistics t > 2.35, we have sufficient evidence to reject H₀.

We conclude at 0.01 level that we have enough evidence to support the claim.