A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 14 people with the condition currently untreated. From this small sample, the mean heart rate is 101 beats per minute with a standard deviation of 8.
(a) Find a 99% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations.
(b) Interpret this confidence interval and write a sentence that explains it.