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.
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)
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