Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 72.4 mmHg (millimeters of mercury) for a sample of size 258 and a sample standard deviation 16.1 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 99% confidence.

Preliminary:

1. Is it safe to assume that n≤5% of all patients with a systolic blood pressure?
   • No
   • Yes
   
   
2. Is n≥30?
   • No
   • Yes

3. Confidence Interval:What is the 99% confidence interval to estimate the population mean? Round your answer to one decimal place IN ORDER TO FIND ANSWER.

?????? < μμ < ?????

Answer 1

Is n >= 30 yes

sample mean, xbar = 72.4
sample standard deviation, s = 16.1
sample size, n = 258
degrees of freedom, df = n - 1 = 257

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.595

ME = tc * s/sqrt(n)
ME = 2.595 * 16.1/sqrt(258)
ME = 2.601

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (72.4 - 2.595 * 16.1/sqrt(258) , 72.4 + 2.595 * 16.1/sqrt(258))
CI = (69.8 , 75)