Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 16.2 mmHg (millimeters of mercury) for a sample of size 476 and a sample standard deviation 18.8 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 98% 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

Confidence Interval:What is the 98% confidence interval to estimate the population mean? ROUND ANSWER TO 1 DECIMAL PLACE!

??? < μ < ????

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 16.2

sample standard deviation = s = 18.8

sample size = n = 476

Degrees of freedom = df = n - 1 = 476 - 1 = 475

a) n≤5% No

n≥30 Yes

b) At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,475 = 2.334

Margin of error = E = t/2,df * (s /n)

= 2.334 * ( 18.8 / 476)

Margin of error = E = 2.0

The 98% confidence interval estimate of the population mean is,

- E < < + E

16.2 - 2.0 < < 16.2 + 2.0

14.2 < < 18.2