Chapter 5, Problem 125P

Hypertension

Blood pressure readings are known to be highly variable. Suppose we have mean SBP for one individual over n visits with k readings per visit $\left({\bar{X}}_{n,k}\right)$. The variability of $\left({\bar{X}}_{n,k}\right)$ depends on n and k and is given by the formula ${\sigma }_w^2={\sigma }_A^2\text{/}n+{\sigma }^2\text{/}(nk)$, where ${\sigma }_A^2$ = between visit variability and σ² = within visit variability. For 30- to 49-year-old Caucasian females, ${\sigma }_A^2=42.9$ and σ² = 12.8. For one individual, we also assume that ${\bar{X}}_{n,k}$ is normally distributed about their true long-term mean = μ with variance = ${\sigma }_w^2$.

It is also known that over a large number of 30- to 49-year-old Caucasian women, their true mean SBP is normally distributed with mean = 120 mm Hg and standard deviation = 14 mm Hg. Also, over a large number of African American 30- to 49-year-old women, their true mean SBP is normal with mean = 130 mm Hg and standard deviation = 20 mm Hg.

Suppose we select a random 30- to 49-year-old Caucasian woman and a random 30- to 49-year-old African American woman. What is the probability that the African American woman has a higher true SBP?

Hint: Use Equation 5.10 (on page 133).