Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 41 for a sample of size 25 and standard deviation 15.

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level).

Give your answers to one decimal place and provide the point estimate with its margin of error.

Answer 1

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level).

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

Where,

Point estimate = Xbar = 41

Margin of error = t*S/sqrt(n)

We are given

Confidence level = 80%

Sample size = n = 25

Standard deviation = S = 15

df = n – 1 = 25 – 1 = 24

Critical t value = 1.3178

Margin of error = t*S/sqrt(n)

Margin of error = 1.3178*15/sqrt(25)

Margin of error = 1.3178*3

Margin of error = 3.9535

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 41 ± 3.9535

Lower limit = 41 - 3.9535 = 37.0465

Upper limit = 41 + 3.9535 = 44.9535

Confidence interval = (37.0, 45.0)