Question

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.7 for a sample of size 438 and standard deviation 16.3.

Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level).


Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).


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Answer 1

21.5≤μ≤25.2

Explanation:

The formula for calculating confidence interval is expressed as;

CI = xbar±(z*s/√n)

xbar is the mean = 23.7

s is the standard deviation= 16.3

n is the sample size = 438

z is the z score at 95% confidence level

z = 1.96

Substitute into the formula

CI = 23.7±(1.96×16.3/√438)

CI = 23.7±(1.96×16.3/20.93)

CI = 23.7±(1.96×0.77788)

CI = 23.7±1.5264

CI = (23.7-1.5264, 23.7+1.5264)

CI = (21.4736, 25.2264)

The confidence interval to the nearest tenth is 21.5≤μ≤25.2