Blood pressure readings are known to be highly variable Supp

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. The variability of (xbar _n,k) depends on n and k and is given by the formula ²_w = ²_A/n + ²/(nk), where ²_A = between visit variability and ² = within visit variability. For 30-to-49 year old white females, ²_A = 42.9 and ² = 12.8. For one individual, we also assume that xbar_n,k is normally distributed about their true long-term mean = m with variance = ²_w.

1. Suppose a woman is measured at two visits with two readings per visit. If her true long-term SBP = 130 mmHg, then what is the probability that her observed mean SBP is >=140?

2. Suppose we want to observe the woman over n visits, where n is sufficiently large so that there is less than a 5% chance that her observed mean SBP will not differ from her true mean SBP by more than than 5 mmHg. What is the smallest value of n to achieve this goal? (Assume two readings per visit)

3. It is also known that over a large number of 30- to 40- year old white women, their true mean SBP is normally distributed with mean = 120 mmHg and standard deviation = 14 mmHg. Also, over a large number of black 30-to49-year old women, their true mean SBP is normal with mean = 130 mmHg and standard deviation = 20 mmHg.

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

Solution