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 based on 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.

$n=157\\\bar x=146\\s=27$

The hypothesis tested are,

$H_0:\mu=140\\vs\\H_1:\mu\gt140$

The test statistic is given as,

$t={\bar x-\mu\over{s\over\sqrt{n}}}={146-140\over{27\over\sqrt{157}}}={6\over2.155}=2.7844$

The critical value is the t distribution table value at $\alpha=0.01$with $n-1=157-1=156$ degrees of freedom given as, $t_{0.01,156}= 2.350489$

The null hypothesis is rejected if, $t\gt t_{0.01,156}$

For this case, $t=2.7844\gt t_{0.01,156}=2.350489$ thus, we reject the null hypothesis and conclude that there is sufficient evidence to show that the mean systolic blood pressure for a population of African American is greater than 140 at 1% significance level.