Chapter 5, Problem 66P

A doctor diagnoses a patient as hypertensive and prescribes an antihypertensive medication. To assess the clinical status of the patient, the doctor takes n replicate blood-pressure measurements before the patient starts the drug (baseline) and n replicate blood-pressure measurements 4 weeks after starting the drug (follow-up). She uses the average of the n replicates at baseline minus the average of the n replicates at follow-up to assess the clinical status of the patient. She knows, from previous clinical experience with the drug, that the mean diastolic blood pressure (DBP) change over a 4-week period over a large number of patients after starting the drug is 5.0 mm Hg with variance 33/n, where n is the number of replicate measures obtained at both baseline and follow-up.

The physician also knows that if a patient is untreated (or does not take the prescribed medication), then the mean DBP over 4 weeks will decline by 2 mm Hg with variance 33/n. What is the probability that an untreated subject will decline by at least 5 mm Hg if 1 replicate measure is obtained at both baseline and follow-up?